notebooks/numbers.ipynb

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    "<a id=\"numbers\"></a>\n",
    "# Numbers\n",
    "Numbers in Python are either *integers*, which are signed whole numbers, and *real numbers* that can have a fractional part. \n",
    "When you do arithmetic on them you can use either of the types."
   ]
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   "source": [
    "x = 5 + 3.2\n",
    "print(\"5 + 3.2 is \", x)"
   ]
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   "source": [
    "## Number operators\n",
    "The usual [arithmetic operators](./arithmetic.ipynb/#Operations-on-numbers) can be used, like addition `+` and subtraction `-`. \n"
   ]
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   "source": [
    "x = 5 + 3\n",
    "print(\"5 + 3 is \", x)\n",
    "x = 4 - 1\n",
    "print(\"4 - 1 is \", x)"
   ]
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   "source": [
    "You can do multiplication with `*` instead of `x`. "
   ]
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   "source": [
    "x = 4 * 3.2\n",
    "print(\"4 * 3.2 is \", x)"
   ]
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   "source": [
    "We do division with `\\` instead of $\\div$."
   ]
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   "source": [
    "x = x / 2.0\n",
    "print(\"x / 2.0 is \", x)"
   ]
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   "source": [
    "There are some special operators on numbers. \n",
    "We compute exponentials, say $3^2$, like this."
   ]
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   "source": [
    "x = 3**2\n",
    "print(\"3**2 is \", x)"
   ]
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   "source": [
    "Another number operator is *modulo*, like \"9 modulo 2\", which gives the remainder after dividing 9 by 2. \n",
    "You can do modulo operations with `%`."
   ]
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   "source": [
    "x = 9 % 2\n",
    "print(\"9 % 2 is \", x)"
   ]
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   "source": [
    "## Operator shortcuts\n",
    "Some operators are used to change a variable's value, like `x = x + 1`. \n",
    "There is a shortcut for each of the operators `+`, `-`, `*`, `/`, `**`, and `%`.\n",
    "\n",
    "For addition, `x = x + 1`, the shortcut is `x += 1`. "
   ]
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   "source": [
    "x = 3\n",
    "print(\"x starts as \", x)\n",
    "x += 2\n",
    "print(\"after x += 2, x is \", x)"
   ]
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   "source": [
    "For subtraction, `x = x - 1`, the shortcut is `x -= 1`"
   ]
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    "x -= 1\n",
    "print(\"after x -= 1, x is \", x)"
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   "source": [
    "For multiplication, `x = x * 4`, the shortcut is `x *= 4`."
   ]
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    "x *= 4\n",
    "print(\"after x *= 4, x is \", x)"
   ]
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   "source": [
    "For division, `x = x / 1`, the shortcut is `x /= 1`."
   ]
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   "source": [
    "x /= 4\n",
    "print(\"after x /= 4, x is \", x)"
   ]
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   "source": [
    "For applying exponents, `x = x ** 2`, the shortcut is `x **= 2`."
   ]
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   "source": [
    "x **= 2\n",
    "print(\"after x **= 2, x is \", x)"
   ]
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   "source": [
    "For `x = x + 3`, the shortcut is `x += 3`."
   ]
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   "source": [
    "x %= 3\n",
    "print(\"after x %= 3, x is \", x)"
   ]
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   "source": [
    "## Number functions"
   ]
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   "source": [
    "### `abs` function\n",
    "The `abs` function is a function that gives a value when it is done. It takes a number that might be negative and gives the absolute value of it."
   ]
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     "text": [
      "abs( 3 ) is  3\n",
      "abs( -5 ) is  5\n",
      "abs( -4.3 ) is  4.3\n"
     ]
    }
   ],
   "source": [
    "x = 3\n",
    "y = -5\n",
    "z = -4.3\n",
    "print(\"abs(\", x, \") is \", abs(x))\n",
    "print(\"abs(\", y, \") is \", abs(y))\n",
    "print(\"abs(\", z, \") is \", abs(z))"
   ]
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   "source": [
    "### `max` function\n",
    "The value of the `max` function is the largest of the numbers give given to it as an argument.\n",
    "`(1, 12, 9)` is a *list* of numbers, which is discussed further below."
   ]
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     "text": [
      "the maximum of  (1, 12, 9)  is  12\n"
     ]
    }
   ],
   "source": [
    "L = (1, 12, 9)\n",
    "print(\"the maximum of \", L, \" is \", max(L))"
   ]
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   "source": [
    "### `min` function\n",
    "The value of the `min` function is the smallest of the numbers give given to it as an argument."
   ]
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     "text": [
      "the minimum of  (1, 12, 9)  is  1\n"
     ]
    }
   ],
   "source": [
    "L = (1, 12, 9)\n",
    "print(\"the minimum of \", L, \" is \", min(L))"
   ]
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    "### `round` function\n",
    "The `round` function takes a real number and reduces the size of the fraction. \n",
    "It gives the integer value without the fraction if only the number is given as the argument. \n",
    "If a second argument is a number, it will keep this many digits in the fractional part."
   ]
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     "text": [
      "round( 5.34 ) is  5\n",
      "round( 9.2345 , 2) is  9.23\n",
      "round( -8.431 ) is  -8\n"
     ]
    }
   ],
   "source": [
    "x = 5.34\n",
    "y = 9.2345\n",
    "z = -8.431\n",
    "print(\"round(\", x, \") is \", round(x))\n",
    "print(\"round(\", y, \", 2) is \", round(y, 2))\n",
    "print(\"round(\", z, \") is \", round(z))"
   ]
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