diff --git a/05_numbers.ipynb b/05_numbers.ipynb
index df7598c..d6409ba 100644
--- a/05_numbers.ipynb
+++ b/05_numbers.ipynb
@@ -92,7 +92,7 @@
     {
      "data": {
       "text/plain": [
-       "140218620396752"
+       "139928698315984"
       ]
      },
      "execution_count": 2,
@@ -2115,7 +2115,7 @@
     {
      "data": {
       "text/plain": [
-       "140218620574432"
+       "139928698489496"
       ]
      },
      "execution_count": 63,
@@ -4070,7 +4070,7 @@
     }
    },
    "source": [
-    "[getcontext()](https://docs.python.org/3/library/decimal.html#decimal.getcontext) shows us how the [decimal](https://docs.python.org/3/library/decimal.html) module is set up. By default, the precision is set to $28$ significant digits, which is roughly twice as many as with `float` objects."
+    "[getcontext()](https://docs.python.org/3/library/decimal.html#decimal.getcontext) shows us how the [decimal](https://docs.python.org/3/library/decimal.html) module is set up. By default, the precision is set to `28` significant digits, which is roughly twice as many as with `float` objects."
    ]
   },
   {
@@ -4282,7 +4282,7 @@
     }
    },
    "source": [
-    "Arithmetic operations between `Decimal` and `int` objects work as the latter are inherently precise: The results are *new* `Decimal` objects."
+    "`Decimal` numbers *preserve* the **significant digits**, even in cases where this is not needed."
    ]
   },
   {
@@ -4290,14 +4290,14 @@
    "execution_count": 137,
    "metadata": {
     "slideshow": {
-     "slide_type": "slide"
+     "slide_type": "fragment"
     }
    },
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "Decimal('42')"
+       "Decimal('0.30000')"
       ]
      },
      "execution_count": 137,
@@ -4306,7 +4306,7 @@
     }
    ],
    "source": [
-    "42 + Decimal(42) - 42"
+    "Decimal(\"0.10000\") + Decimal(\"0.20000\")"
    ]
   },
   {
@@ -4321,7 +4321,7 @@
     {
      "data": {
       "text/plain": [
-       "Decimal('42')"
+       "True"
       ]
      },
      "execution_count": 138,
@@ -4330,7 +4330,18 @@
     }
    ],
    "source": [
-    "10 * Decimal(42) / 10"
+    "Decimal(\"0.10000\") + Decimal(\"0.20000\") == Decimal(\"0.3\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "source": [
+    "Arithmetic operations between `Decimal` and `int` objects work as the latter are inherently precise: The results are *new* `Decimal` objects."
    ]
   },
   {
@@ -4345,7 +4356,7 @@
     {
      "data": {
       "text/plain": [
-       "Decimal('0.1')"
+       "Decimal('42')"
       ]
      },
      "execution_count": 139,
@@ -4353,6 +4364,54 @@
      "output_type": "execute_result"
     }
    ],
+   "source": [
+    "42 + Decimal(42) - 42"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 140,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "-"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Decimal('42')"
+      ]
+     },
+     "execution_count": 140,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "10 * Decimal(42) / 10"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 141,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Decimal('0.1')"
+      ]
+     },
+     "execution_count": 141,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "Decimal(1) / 10"
    ]
@@ -4370,7 +4429,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 140,
+   "execution_count": 142,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4383,7 +4442,7 @@
        "'0.10000000000000000000000000000000000000000000000000'"
       ]
      },
-     "execution_count": 140,
+     "execution_count": 142,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4394,7 +4453,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 141,
+   "execution_count": 143,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -4407,7 +4466,7 @@
        "'0.10000000000000000555111512312578270211815834045410'"
       ]
      },
-     "execution_count": 141,
+     "execution_count": 143,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4429,7 +4488,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 142,
+   "execution_count": 144,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -4443,7 +4502,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-142-a3cea145e6d1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;36m1.0\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m42\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-144-a3cea145e6d1>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;36m1.0\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m42\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
       "\u001b[0;31mTypeError\u001b[0m: unsupported operand type(s) for *: 'float' and 'decimal.Decimal'"
      ]
     }
@@ -4465,7 +4524,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 143,
+   "execution_count": 145,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -4478,7 +4537,7 @@
        "Decimal('2')"
       ]
      },
-     "execution_count": 143,
+     "execution_count": 145,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4489,7 +4548,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 144,
+   "execution_count": 146,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -4502,7 +4561,7 @@
        "Decimal('1.414213562373095048801688724')"
       ]
      },
-     "execution_count": 144,
+     "execution_count": 146,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4526,7 +4585,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 145,
+   "execution_count": 147,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4539,7 +4598,7 @@
        "Decimal('1.999999999999999999999999999')"
       ]
      },
-     "execution_count": 145,
+     "execution_count": 147,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4558,14 +4617,14 @@
     }
    },
    "source": [
-    "The [quantize()](https://docs.python.org/3/library/decimal.html#decimal.Decimal.quantize) method allows us to cut off a `Decimal` number at any digit that is smaller than the set precision while adhering to the rounding rules from math.\n",
+    "The [quantize()](https://docs.python.org/3/library/decimal.html#decimal.Decimal.quantize) method allows us to [quantize](https://www.dictionary.com/browse/quantize) (i.e., \"round\") a `Decimal` number at any precision that is *smaller* than the set precision. It looks at the number of decimals (i.e., to the right of the period) of the numeric argument we pass in.\n",
     "\n",
-    "For example, as the overall imprecise value of `two` still has a precision of $28$ digits, we can correctly round it to the first $20$ digits."
+    "For example, as the overall imprecise value of `two` still has an internal precision of `28` digits, we can correctly round it to *four* decimals (i.e., `Decimal(\"0.0001\")` has four decimals)."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 146,
+   "execution_count": 148,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4575,16 +4634,44 @@
     {
      "data": {
       "text/plain": [
-       "Decimal('2')"
+       "Decimal('2.0000')"
       ]
      },
-     "execution_count": 146,
+     "execution_count": 148,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "two.quantize(20)"
+    "two.quantize(Decimal(\"0.0001\"))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can never round a `Decimal` number and obtain a greater precision than before: The `InvalidOperation` exception tells us that *loudly*."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 149,
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "InvalidOperation",
+     "evalue": "[<class 'decimal.InvalidOperation'>]",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mInvalidOperation\u001b[0m                          Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-149-11848d4ba22a>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtwo\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mquantize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"0.1\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m28\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;31mInvalidOperation\u001b[0m: [<class 'decimal.InvalidOperation'>]"
+     ]
+    }
+   ],
+   "source": [
+    "two.quantize(Decimal(\"0.1\") ** 28)"
    ]
   },
   {
@@ -4595,12 +4682,12 @@
     }
    },
    "source": [
-    "Consequently, with this little workaround $\\sqrt{2}^2 = 2$ works even in Python."
+    "Consequently, with this little workaround $\\sqrt{2}^2 = 2$ works, even in Python."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 147,
+   "execution_count": 150,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4613,13 +4700,13 @@
        "True"
       ]
      },
-     "execution_count": 147,
+     "execution_count": 150,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "two.quantize(20) == 2"
+    "two.quantize(Decimal(\"0.0001\")) == 2"
    ]
   },
   {
@@ -4635,7 +4722,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 148,
+   "execution_count": 151,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4648,13 +4735,13 @@
        "True"
       ]
      },
-     "execution_count": 148,
+     "execution_count": 151,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "(Decimal(2).sqrt() ** 2).quantize(20) == 2"
+    "(Decimal(2).sqrt() ** 2).quantize(Decimal(\"0.0001\")) == 2"
    ]
   },
   {
@@ -4670,7 +4757,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 149,
+   "execution_count": 152,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4683,85 +4770,13 @@
        "Decimal('NaN')"
       ]
      },
-     "execution_count": 149,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Decimal(\"nan\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 150,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "False"
-      ]
-     },
-     "execution_count": 150,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Decimal(\"nan\") == Decimal(\"nan\")  # nan's never compare equal to anything, not even to themselves"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 151,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Decimal('Infinity')"
-      ]
-     },
-     "execution_count": 151,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "Decimal(\"inf\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 152,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "Decimal('-Infinity')"
-      ]
-     },
      "execution_count": 152,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "Decimal(\"-inf\")"
+    "Decimal(\"nan\")"
    ]
   },
   {
@@ -4776,7 +4791,7 @@
     {
      "data": {
       "text/plain": [
-       "Decimal('Infinity')"
+       "False"
       ]
      },
      "execution_count": 153,
@@ -4785,7 +4800,7 @@
     }
    ],
    "source": [
-    "Decimal(\"inf\") + 42  # Infinity is infinity, concrete numbers loose its meaning"
+    "Decimal(\"nan\") == Decimal(\"nan\")  # nan's never compare equal to anything, not even to themselves"
    ]
   },
   {
@@ -4800,7 +4815,7 @@
     {
      "data": {
       "text/plain": [
-       "True"
+       "Decimal('Infinity')"
       ]
      },
      "execution_count": 154,
@@ -4808,6 +4823,78 @@
      "output_type": "execute_result"
     }
    ],
+   "source": [
+    "Decimal(\"inf\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 155,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Decimal('-Infinity')"
+      ]
+     },
+     "execution_count": 155,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Decimal(\"-inf\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 156,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Decimal('Infinity')"
+      ]
+     },
+     "execution_count": 156,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "Decimal(\"inf\") + 42  # Infinity is infinity, concrete numbers loose its meaning"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 157,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "True"
+      ]
+     },
+     "execution_count": 157,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "Decimal(\"inf\") + 42 == Decimal(\"inf\")"
    ]
@@ -4825,7 +4912,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 155,
+   "execution_count": 158,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4839,7 +4926,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mInvalidOperation\u001b[0m                          Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-155-87950ebbd6ef>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"-inf\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-158-87950ebbd6ef>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"-inf\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
       "\u001b[0;31mInvalidOperation\u001b[0m: [<class 'decimal.InvalidOperation'>]"
      ]
     }
@@ -4850,7 +4937,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 156,
+   "execution_count": 159,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -4864,7 +4951,7 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mInvalidOperation\u001b[0m                          Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-156-996083f200c6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-159-996083f200c6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mDecimal\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"inf\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
       "\u001b[0;31mInvalidOperation\u001b[0m: [<class 'decimal.InvalidOperation'>]"
      ]
     }
@@ -4910,7 +4997,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 157,
+   "execution_count": 160,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -4934,7 +5021,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 158,
+   "execution_count": 161,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -4947,7 +5034,7 @@
        "Fraction(1, 3)"
       ]
      },
-     "execution_count": 158,
+     "execution_count": 161,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4958,7 +5045,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 159,
+   "execution_count": 162,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -4971,7 +5058,7 @@
        "Fraction(1, 3)"
       ]
      },
-     "execution_count": 159,
+     "execution_count": 162,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -4982,7 +5069,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 160,
+   "execution_count": 163,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -4995,7 +5082,7 @@
        "Fraction(3333333333, 10000000000)"
       ]
      },
-     "execution_count": 160,
+     "execution_count": 163,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5006,7 +5093,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 161,
+   "execution_count": 164,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5019,7 +5106,7 @@
        "Fraction(3333333333, 10000000000)"
       ]
      },
-     "execution_count": 161,
+     "execution_count": 164,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5041,7 +5128,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 162,
+   "execution_count": 165,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5054,7 +5141,7 @@
        "Fraction(3, 2)"
       ]
      },
-     "execution_count": 162,
+     "execution_count": 165,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5065,7 +5152,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 163,
+   "execution_count": 166,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5078,7 +5165,7 @@
        "Fraction(3, 2)"
       ]
      },
-     "execution_count": 163,
+     "execution_count": 166,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5100,7 +5187,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 164,
+   "execution_count": 167,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5113,7 +5200,7 @@
        "Fraction(1, 10)"
       ]
      },
-     "execution_count": 164,
+     "execution_count": 167,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5135,7 +5222,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 165,
+   "execution_count": 168,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5148,7 +5235,7 @@
        "Fraction(3602879701896397, 36028797018963968)"
       ]
      },
-     "execution_count": 165,
+     "execution_count": 168,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5170,7 +5257,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 166,
+   "execution_count": 169,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5183,7 +5270,7 @@
        "Fraction(7, 4)"
       ]
      },
-     "execution_count": 166,
+     "execution_count": 169,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5194,7 +5281,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 167,
+   "execution_count": 170,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5207,7 +5294,7 @@
        "Fraction(1, 2)"
       ]
      },
-     "execution_count": 167,
+     "execution_count": 170,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5218,7 +5305,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 168,
+   "execution_count": 171,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5231,7 +5318,7 @@
        "Fraction(1, 1)"
       ]
      },
-     "execution_count": 168,
+     "execution_count": 171,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5242,7 +5329,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 169,
+   "execution_count": 172,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5255,7 +5342,7 @@
        "Fraction(1, 1)"
       ]
      },
-     "execution_count": 169,
+     "execution_count": 172,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5277,7 +5364,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 170,
+   "execution_count": 173,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5290,7 +5377,7 @@
        "0.1"
       ]
      },
-     "execution_count": 170,
+     "execution_count": 173,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5301,7 +5388,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 171,
+   "execution_count": 174,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5314,7 +5401,7 @@
        "'0.10000000000000000555111512312578270211815834045410'"
       ]
      },
-     "execution_count": 171,
+     "execution_count": 174,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5383,12 +5470,12 @@
    "source": [
     "`complex` numbers are part of core Python. The simplest way to create one is to write an arithmetic expression with the literal `j` notation for $\\textbf{i}$. The `j` is commonly used in many engineering disciplines instead of the symbol $\\textbf{i}$ from math as $I$ in engineering more often than not means [electric current](https://en.wikipedia.org/wiki/Electric_current).\n",
     "\n",
-    "For example, the answer to $x^2 = -1$ can be written in Python as `1j` like below. This creates a `complex` object with value `1j`. The same syntactic rules apply as with the above `e` notation: No spaces are allowed between the number and the `j`, and the number may be any `int` or `float` literal."
+    "For example, the answer to $x^2 = -1$ can be written in Python as `1j` like below. This creates a `complex` object with value `1j`. The same syntactic rules apply as with the above `e` notation: No spaces are allowed between the number and the `j`. The number may be any `int` or `float` literal; however, it is stored as a `float` internally. So, `complex` numbers suffer from the same imprecision as `float` numbers."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 172,
+   "execution_count": 175,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5401,7 +5488,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 173,
+   "execution_count": 176,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5411,10 +5498,10 @@
     {
      "data": {
       "text/plain": [
-       "140218611341648"
+       "139928697740272"
       ]
      },
-     "execution_count": 173,
+     "execution_count": 176,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5425,7 +5512,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 174,
+   "execution_count": 177,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5438,7 +5525,7 @@
        "complex"
       ]
      },
-     "execution_count": 174,
+     "execution_count": 177,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5449,7 +5536,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 175,
+   "execution_count": 178,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5462,7 +5549,7 @@
        "1j"
       ]
      },
-     "execution_count": 175,
+     "execution_count": 178,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5484,7 +5571,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 176,
+   "execution_count": 179,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5497,7 +5584,7 @@
        "True"
       ]
      },
-     "execution_count": 176,
+     "execution_count": 179,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5519,7 +5606,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 177,
+   "execution_count": 180,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5532,7 +5619,7 @@
        "(2+0.5j)"
       ]
      },
-     "execution_count": 177,
+     "execution_count": 180,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5554,7 +5641,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 178,
+   "execution_count": 181,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5567,7 +5654,7 @@
        "(2+0.5j)"
       ]
      },
-     "execution_count": 178,
+     "execution_count": 181,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5578,7 +5665,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 179,
+   "execution_count": 182,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5591,7 +5678,7 @@
        "(2+0j)"
       ]
      },
-     "execution_count": 179,
+     "execution_count": 182,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5602,7 +5689,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 180,
+   "execution_count": 183,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5615,7 +5702,7 @@
        "(2+0.5j)"
       ]
      },
-     "execution_count": 180,
+     "execution_count": 183,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5626,7 +5713,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 181,
+   "execution_count": 184,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -5639,7 +5726,7 @@
        "(2+0.5j)"
       ]
      },
-     "execution_count": 181,
+     "execution_count": 184,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5661,7 +5748,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 182,
+   "execution_count": 185,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5675,7 +5762,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 183,
+   "execution_count": 186,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5688,7 +5775,7 @@
        "(4+6j)"
       ]
      },
-     "execution_count": 183,
+     "execution_count": 186,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5699,7 +5786,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 184,
+   "execution_count": 187,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5712,85 +5799,13 @@
        "(-2-2j)"
       ]
      },
-     "execution_count": 184,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "c1 - c2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 185,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(40+2j)"
-      ]
-     },
-     "execution_count": 185,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "c1 + 39"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 186,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "-4j"
-      ]
-     },
-     "execution_count": 186,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "3.0 - c2"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 187,
-   "metadata": {
-    "slideshow": {
-     "slide_type": "skip"
-    }
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(5+10j)"
-      ]
-     },
      "execution_count": 187,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "5 * c1"
+    "c1 - c2"
    ]
   },
   {
@@ -5805,7 +5820,7 @@
     {
      "data": {
       "text/plain": [
-       "(0.5+0.6666666666666666j)"
+       "(40+2j)"
       ]
      },
      "execution_count": 188,
@@ -5813,13 +5828,85 @@
      "output_type": "execute_result"
     }
    ],
+   "source": [
+    "c1 + 39"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 189,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "-4j"
+      ]
+     },
+     "execution_count": 189,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "3.0 - c2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 190,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(5+10j)"
+      ]
+     },
+     "execution_count": 190,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "5 * c1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 191,
+   "metadata": {
+    "slideshow": {
+     "slide_type": "skip"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(0.5+0.6666666666666666j)"
+      ]
+     },
+     "execution_count": 191,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "c2 / 6"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 189,
+   "execution_count": 192,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5832,7 +5919,7 @@
        "(-5+10j)"
       ]
      },
-     "execution_count": 189,
+     "execution_count": 192,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5843,7 +5930,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 190,
+   "execution_count": 193,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5856,7 +5943,7 @@
        "(0.44+0.08j)"
       ]
      },
-     "execution_count": 190,
+     "execution_count": 193,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5878,7 +5965,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 191,
+   "execution_count": 194,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -5891,7 +5978,7 @@
        "5.0"
       ]
      },
-     "execution_count": 191,
+     "execution_count": 194,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5913,7 +6000,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 192,
+   "execution_count": 195,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5926,7 +6013,7 @@
        "1.0"
       ]
      },
-     "execution_count": 192,
+     "execution_count": 195,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5937,7 +6024,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 193,
+   "execution_count": 196,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -5950,7 +6037,7 @@
        "2.0"
       ]
      },
-     "execution_count": 193,
+     "execution_count": 196,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -5972,7 +6059,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 194,
+   "execution_count": 197,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -5985,7 +6072,7 @@
        "(1-2j)"
       ]
      },
-     "execution_count": 194,
+     "execution_count": 197,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6062,7 +6149,7 @@
     "\n",
     "For the other types, in particular, the `float` type, the implications of their imprecision are discussed in detail above.\n",
     "\n",
-    "The abstract concepts behind the four outer-most mathematical sets are part of Python since [PEP 3141](https://www.python.org/dev/peps/pep-3141/) in 2007. The [numbers](https://docs.python.org/3/library/numbers.html) module in the [standard library](https://docs.python.org/3/library/index.html) defines what Pythonistas call the **numeric tower**, a collection of five **[abstract data types](https://en.wikipedia.org/wiki/Abstract_data_type)**, or **abstract base classes** as they are called in Python slang:\n",
+    "The abstract concepts behind the four outer-most mathematical sets are part of Python since [PEP 3141](https://www.python.org/dev/peps/pep-3141/) in 2007. The [numbers](https://docs.python.org/3/library/numbers.html) module in the [standard library](https://docs.python.org/3/library/index.html) defines what Pythonistas call the **numeric tower**, a collection of five **[abstract data types](https://en.wikipedia.org/wiki/Abstract_data_type)**, or **abstract base classes** as they are called in Python jargon:\n",
     "\n",
     "- `numbers.Number`: \"any number\" (cf., [documentation](https://docs.python.org/3/library/numbers.html#numbers.Number))\n",
     "- `numbers.Complex`: \"all complex numbers\" (cf., [documentation](https://docs.python.org/3/library/numbers.html#numbers.Complex))\n",
@@ -6073,7 +6160,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 195,
+   "execution_count": 198,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6086,7 +6173,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 196,
+   "execution_count": 199,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -6114,7 +6201,7 @@
        " 'abstractmethod']"
       ]
      },
-     "execution_count": 196,
+     "execution_count": 199,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6140,7 +6227,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 197,
+   "execution_count": 200,
    "metadata": {
     "scrolled": true,
     "slideshow": {
@@ -6262,7 +6349,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 198,
+   "execution_count": 201,
    "metadata": {
     "slideshow": {
      "slide_type": "skip"
@@ -6429,7 +6516,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 199,
+   "execution_count": 202,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6442,7 +6529,7 @@
        "True"
       ]
      },
-     "execution_count": 199,
+     "execution_count": 202,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6453,7 +6540,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 200,
+   "execution_count": 203,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6466,7 +6553,7 @@
        "True"
       ]
      },
-     "execution_count": 200,
+     "execution_count": 203,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6477,7 +6564,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 201,
+   "execution_count": 204,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -6490,7 +6577,7 @@
        "True"
       ]
      },
-     "execution_count": 201,
+     "execution_count": 204,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6501,7 +6588,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 202,
+   "execution_count": 205,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -6514,7 +6601,7 @@
        "True"
       ]
      },
-     "execution_count": 202,
+     "execution_count": 205,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6536,7 +6623,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 203,
+   "execution_count": 206,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6549,7 +6636,7 @@
        "False"
       ]
      },
-     "execution_count": 203,
+     "execution_count": 206,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6571,7 +6658,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 204,
+   "execution_count": 207,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6584,7 +6671,7 @@
        "True"
       ]
      },
-     "execution_count": 204,
+     "execution_count": 207,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6595,7 +6682,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 205,
+   "execution_count": 208,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -6608,7 +6695,7 @@
        "False"
       ]
      },
-     "execution_count": 205,
+     "execution_count": 208,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6641,7 +6728,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 206,
+   "execution_count": 209,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6654,7 +6741,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 207,
+   "execution_count": 210,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -6667,7 +6754,7 @@
        "0"
       ]
      },
-     "execution_count": 207,
+     "execution_count": 210,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6678,7 +6765,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 208,
+   "execution_count": 211,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6703,7 +6790,7 @@
     "    if not isinstance(n, numbers.Integral):\n",
     "        if isinstance(n, numbers.Real):\n",
     "            if n != math.trunc(n) and strict:\n",
-    "                raise ValueError(\"n is not an integer-like value; it has decimals\")\n",
+    "                raise TypeError(\"n is not an integer-like value; it has decimals\")\n",
     "            n = math.trunc(n)\n",
     "        else:\n",
     "            raise TypeError(\"Factorial is only defined for integers\")\n",
@@ -6728,7 +6815,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 209,
+   "execution_count": 212,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6741,7 +6828,7 @@
        "1"
       ]
      },
-     "execution_count": 209,
+     "execution_count": 212,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6752,7 +6839,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 210,
+   "execution_count": 213,
    "metadata": {
     "slideshow": {
      "slide_type": "-"
@@ -6765,7 +6852,7 @@
        "6"
       ]
      },
-     "execution_count": 210,
+     "execution_count": 213,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6776,7 +6863,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 211,
+   "execution_count": 214,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6789,7 +6876,7 @@
        "6"
       ]
      },
-     "execution_count": 211,
+     "execution_count": 214,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6811,7 +6898,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 212,
+   "execution_count": 215,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6819,15 +6906,15 @@
    },
    "outputs": [
     {
-     "ename": "ValueError",
+     "ename": "TypeError",
      "evalue": "n is not an integer-like value; it has decimals",
      "output_type": "error",
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-212-188b816be8b6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m<ipython-input-208-65a2caa81b4a>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n, strict)\u001b[0m\n\u001b[1;32m     16\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mReal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mstrict\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"n is not an integer-like value; it has decimals\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m             \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
-      "\u001b[0;31mValueError\u001b[0m: n is not an integer-like value; it has decimals"
+      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
+      "\u001b[0;32m<ipython-input-215-188b816be8b6>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3.1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-211-60ca579e64ac>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n, strict)\u001b[0m\n\u001b[1;32m     16\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnumbers\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mReal\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     17\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mstrict\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 18\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"n is not an integer-like value; it has decimals\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     19\u001b[0m             \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mTypeError\u001b[0m: n is not an integer-like value; it has decimals"
      ]
     }
    ],
@@ -6837,7 +6924,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 213,
+   "execution_count": 216,
    "metadata": {
     "slideshow": {
      "slide_type": "fragment"
@@ -6850,7 +6937,7 @@
        "6"
       ]
      },
-     "execution_count": 213,
+     "execution_count": 216,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -6872,7 +6959,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 214,
+   "execution_count": 217,
    "metadata": {
     "slideshow": {
      "slide_type": "slide"
@@ -6886,8 +6973,8 @@
      "traceback": [
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[0;32m<ipython-input-214-7296a74f5dcf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2j\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;32m<ipython-input-208-65a2caa81b4a>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n, strict)\u001b[0m\n\u001b[1;32m     19\u001b[0m             \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 21\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is only defined for integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     22\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;32m<ipython-input-217-7296a74f5dcf>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mfactorial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m2j\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m<ipython-input-211-60ca579e64ac>\u001b[0m in \u001b[0;36mfactorial\u001b[0;34m(n, strict)\u001b[0m\n\u001b[1;32m     19\u001b[0m             \u001b[0mn\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmath\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     20\u001b[0m         \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 21\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Factorial is only defined for integers\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     22\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mn\u001b[0m \u001b[0;34m<\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
       "\u001b[0;31mTypeError\u001b[0m: Factorial is only defined for integers"
      ]
     }
@@ -6924,7 +7011,7 @@
     "- `Decimal`: similar to `float` but allows customizing the precision; still inherently imprecise\n",
     "- `Fraction`: a perfect model for rational numbers (i.e., the set $\\mathbb{Q}$); built on top of the `int` type and therefore inherently precise\n",
     "\n",
-    "The important takeaways for the data science practicioner are:\n",
+    "The *important* takeaways for the data science practitioner are:\n",
     "\n",
     "1. **Do not mix** precise and imprecise data types, and\n",
     "2. actively expect `nan` results when working with `float` numbers as there are no **loud failures**.\n",
diff --git a/05_numbers_review_and_exercises.ipynb b/05_numbers_review_and_exercises.ipynb
new file mode 100644
index 0000000..4246965
--- /dev/null
+++ b/05_numbers_review_and_exercises.ipynb
@@ -0,0 +1,722 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "# Chapter 5: Numbers"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Content Review"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Read [Chapter 5](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/05_numbers.ipynb) of the book. Then work through the eighteen review questions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Essay Questions "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Answer the following questions briefly with *at most* 300 characters per question!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q1**: In what way is the **binary representation** of `int` objects *similar* to the **decimal system** taught in elementary school?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q2**: Why may objects of type `bool` be regarded a **numeric type** as well?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q3**: Why is it *inefficient* to store `bool` objects in bits resembling a **hexadecimal representation**?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q4**: Colors are commonly expressed in the **hexadecimal system** in websites (cf., the [HTML](https://en.wikipedia.org/wiki/HTML) and [CSS](https://en.wikipedia.org/wiki/Cascading_Style_Sheets) formats).\n",
+    "\n",
+    "For example, $#000000$, $#ff9900$, and $#ffffff$ turn out to be black, orange, and white. The six digits are read in *pairs of two* from left to right, and the *three pairs* correspond to the proportions of red, green, and blue mixed together. They reach from $0_{16} = 0_{10}$ for $0$% to $\\text{ff}_{16} = 255_{10}$ for $100$% (cf., this [article](https://en.wikipedia.org/wiki/RGB_color_model) for an in-depth discussion).\n",
+    "\n",
+    "In percent, what are the proportions of red, green, and blue that make up orange? Calculate the three percentages separately! How many **bytes** are needed to encode a color? How many **bits** are that?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q5**: What does it mean for a code fragment to **fail silently**?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q6**: Explain why the mathematical set of all real numbers $\\mathbb{R}$ can only be **approximated** by floating-point numbers on a computer!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q7**: How do we deal with a `float` object's imprecision if we need to **check for equality**?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q8**: What data type, built-in or from the [standard library](https://docs.python.org/3/library/index.html), is best suited to represent the [transcendental numbers](https://en.wikipedia.org/wiki/Transcendental_number) $\\pi$ and $\\text{e}$?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q9**: How can **abstract data types**, for example, as defined in the **numeric tower**, be helpful in enabling **duck typing**?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### True / False Questions"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Motivate your answer with *one short* sentence!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q10**: The precision of `int` objects depends on how we choose to represent them in memory. For example, using a **hexadecimal representation** gives us $16^8$ digits whereas with a **binary representation** an `int` object can have *at most* $2^8$ digits."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q11**: With the built-in [round()](https://docs.python.org/3/library/functions.html#round) function, we obtain a *precise* representation for any `float` object if we can live with *less than* $15$ digits of precision."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q12**: As most currencies operate with $2$ or $3$ decimals (e.g., EUR $9.99$), the `float` type's limitation of *at most* $15$ digits is *not* a problem in practice."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q13**: The [IEEE 754](https://en.wikipedia.org/wiki/IEEE_754) standard's **special values** provide no benefit in practice as we could always use a **[sentinel](https://en.wikipedia.org/wiki/Sentinel_value)** value (i.e., a \"dummy\"). For example, instead of `nan`, we can always use `0` to indicate a *missing* value."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q14**: The following code fragment raises an `InvalidOperation` exception. That is an example of code **failing loudly**.\n",
+    "```python\n",
+    "float(\"inf\") + float(\"-inf\")\n",
+    "```"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q15**: Python provides a `scientific` type (e.g., `1.23e4`) that is useful mainly to model problems in the domains of physics or astrophysics."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q16**: From a practitioner's point of view, the built-in [format()](https://docs.python.org/3/library/functions.html#format) function does the *same* as the built-in [round()](https://docs.python.org/3/library/functions.html#round) function."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q17**: The `Decimal` type from the [decimal](https://docs.python.org/3/library/decimal.html) module in the [standard library](https://docs.python.org/3/library/index.html) allows us to model the set of the real numbers $\\mathbb{R}$ *precisely*."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q18**: The `Fraction` type from the [fractions](https://docs.python.org/3/library/fractions.html) module in the [standard library](https://docs.python.org/3/library/index.html) allows us to model the set of the rational numbers $\\mathbb{Q}$ *precisely*."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Coding Exercises"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Discounting Customer Orders (revisited)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q11** in [Chapter 2's Review & Exercises](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/02_functions_review_and_exercises.ipynb#Volume-of-a-Sphere) section already revealed that we must consider the effects of the `float` type's imprecision.\n",
+    "\n",
+    "This becomes even more important when we deal with numeric data modeling accounting or finance data (cf., [this comment](https://stackoverflow.com/a/24976426) on \"falsehoods programmers believe about money\").\n",
+    "\n",
+    "In addition to the *inherent imprecision* of numbers in general, the topic of **[rounding numbers](https://en.wikipedia.org/wiki/Rounding)** is also not as trivial as we might expect! [This article](https://realpython.com/python-rounding/) summarizes everything the data science practitioner needs to know.\n",
+    "\n",
+    "In this exercise, we revisit **Q9** from [Chapter 3's Review & Exercises](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/03_conditionals_review_and_exercises.ipynb#Discounting-Customer-Orders) section, and make the `discounted_price()` function work *correctly* for real-life sales data."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q19.1**: Execute the code cells below! What results would you have *expected*, and why?"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "round(1.5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "round(2.5)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "round(2.675, 2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q19.2**: The built-in [round()](https://docs.python.org/3/library/functions.html#round) function implements the \"**[round half to even](https://en.wikipedia.org/wiki/Rounding#Round_half_to_even)**\" strategy. Describe in one or two sentences what that means!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q19.3**: For the revised `discounted_price()` function, we have to tackle *two* issues: First, we have to replace the built-in `float` type with a data type that allows us to control the precision. Second, the discounted price should be rounded according to a more human-friendly rounding strategy, namely \"**[round half away from zero](https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero)**.\"\n",
+    "\n",
+    "Describe in one or two sentences how \"**[round half away from zero](https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero)**\" is more in line with how humans think of rounding!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    " "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q19.4**: We use the `Decimal` type from the [decimal](https://docs.python.org/3/library/decimal.html) module in the [standard library](https://docs.python.org/3/library/index.html) to tackle *both* issues simultaneously.\n",
+    "\n",
+    "Assign `euro` a numeric object such that both `Decimal(\"1.5\")` and `Decimal(\"2.5\")` are rounded to `Decimal(\"2\")` (i.e., no decimal) with the [quantize()](https://docs.python.org/3/library/decimal.html#decimal.Decimal.quantize) method!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from decimal import Decimal"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "euro = ..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Decimal(\"1.5\").quantize(...)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Decimal(\"2.5\").quantize(...)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q19.5**: Obviously, the two preceding code cells still [round half to even](https://en.wikipedia.org/wiki/Rounding#Round_half_to_even).\n",
+    "\n",
+    "The [decimal](https://docs.python.org/3/library/decimal.html) module defines a `ROUND_HALF_UP` flag that we can pass as the second argument to the [quantize()](https://docs.python.org/3/library/decimal.html#decimal.Decimal.quantize) method. Then, it [rounds half away from zero](https://en.wikipedia.org/wiki/Rounding#Round_half_away_from_zero).\n",
+    "\n",
+    "Add `ROUND_HALF_UP` to the code cells! `Decimal(\"2.5\")` should now be rounded to `Decimal(\"3\")`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from decimal import ROUND_HALF_UP"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Decimal(\"1.5\").quantize(...)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Decimal(\"2.5\").quantize(...)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q19.6**: Instead of `euro`, define `cents` such that rounding occurs to *two* decimals! `Decimal(\"2.675\")` should now be rounded to `Decimal(\"2.68\")`. Do *not* forget to include the `ROUND_HALF_UP` flag!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cents = ..."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "Decimal(\"2.675\").quantize(...)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q19.7**: Re-write the function `discounted_price()` from [Chapter 3's Review & Exercises](https://nbviewer.jupyter.org/github/webartifex/intro-to-python/blob/master/03_conditionals_review_and_exercises.ipynb#Discounting-Customer-Orders) section!\n",
+    "\n",
+    "It takes the *positional* arguments `unit_price` and `quantity` and implements a discount scheme for a line item in a customer order as follows:\n",
+    "\n",
+    "- if the unit price is over 100 dollars, grant 10% relative discount\n",
+    "- if a customer orders more than 10 items, one in every five items is for free\n",
+    "\n",
+    "Only one of the two discounts is granted, whichever is better for the customer.\n",
+    "\n",
+    "The function then returns the overall price for the line item as a `Decimal` number with a precision of *two* decimals.\n",
+    "\n",
+    "Enable **duck typing** by allowing the function to be called with various numeric types as the arguments, in particular, `quantity` may be a non-integer as well: Use an appropriate **abstract data type** from the [numbers](https://docs.python.org/3/library/numbers.html) module in the [standard library](https://docs.python.org/3/library/index.html) to verify the arguments' types and also that they are both positive!\n",
+    "\n",
+    "It is considered a *best practice* to only round towards the *end* of the calculations."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numbers"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def discounted_price(...):\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ...\n",
+    "    ..."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Q19.8**: Execute the code cells below and verify the final price for the following four test cases:\n",
+    "\n",
+    "- $7$ smartphones @ $99.00$ USD\n",
+    "- $3$ workstations @ $999.00$ USD\n",
+    "- $19$ GPUs @ $879.95$ USD\n",
+    "- $14$ Raspberry Pis @ $35.00$ USD\n",
+    "\n",
+    "The output should now *always* be a `Decimal` number with *two* decimals!"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "discounted_price(99, 7)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "discounted_price(999, 3)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "discounted_price(879.95, 19)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "discounted_price(35, 14)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "This also works if `quantity` is passed in as a `float` type."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "discounted_price(99, 7.0)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Decimals beyond the first two are gracefully discarded (i.e., *without* rounding errors accumulating)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "discounted_price(99.0001, 7)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The basic input validation ensures that the user of `discounted_price()` does not pass in invalid data. Here, the `\"abc\"` creates a `TypeError`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "discounted_price(\"abc\", 7)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "A `-1` passed in as `unit_price` results in a `ValueError`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "discounted_price(-1, 7)"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.3"
+  },
+  "toc": {
+   "base_numbering": 1,
+   "nav_menu": {},
+   "number_sections": false,
+   "sideBar": true,
+   "skip_h1_title": true,
+   "title_cell": "Table of Contents",
+   "title_sidebar": "Contents",
+   "toc_cell": false,
+   "toc_position": {},
+   "toc_section_display": false,
+   "toc_window_display": false
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}