13. Numbers and math

Python numbers come in two main kinds, do the usual arithmetic, and plug into standard library modules for more helpers. This chapter covers what you need for game logic: rounding, random numbers, basic maths.

Integers and floats

Python has two common number types:

int. A whole number with no decimal part: 0, 7, -42.
float. A number with a decimal point: 3.14, 0.5, -1.0.

Most of the time you do not have to care which is which. 7 is an int, 7.0 is a float. When you mix them in arithmetic the result is a float.

type(x).__name__ tells you which you have:

print(type(7).__name__)     # int
print(type(7.0).__name__)   # float
print(type(3.14).__name__)  # float

Arithmetic

The familiar operators are all here, plus two less common in everyday maths:

Operator	Name	Example	Result
`+`	addition	`3 + 2`	`5`
`-`	subtraction	`7 - 4`	`3`
`*`	multiplication	`6 * 7`	`42`
`/`	float division	`7 / 2`	`3.5`
`//`	integer division	`7 // 2`	`3`
`%`	modulo (remainder)	`7 % 3`	`1`
`**`	power	`2 ** 8`	`256`

Three are worth a closer look:

Float division / always gives a float in Python, even when the answer is whole. 6 / 3 is 2.0, not 2. This is different from some other languages where dividing two integers gives an integer.

Integer division // drops everything after the decimal point. 7 // 2 is 3. -7 // 2 is -4, because it rounds toward negative infinity, not toward zero.

Modulo % is the remainder after integer division. 7 % 3 is 1 because 7 = 2 * 3 + 1. It is the standard way to ask "is this number even?" — n % 2 is 0 for evens and 1 for odds.

print(7 / 2)    # 3.5
print(7 // 2)   # 3
print(7 % 2)    # 1
print(2 ** 8)   # 256

Open exercises/13/01-arithmetic.py. Predict each printed result before running, then run and check.

The `math` module

Python's math module has the helpers you reach for most. Add import math at the top of your file to use them:

import math

Function	What it does
`math.floor(x)`	Largest integer not greater than `x`. `floor(3.7) -> 3`.
`math.ceil(x)`	Smallest integer not less than `x`. `ceil(3.2) -> 4`.
`abs(x)`	The absolute value. `abs(-5) -> 5`. Built-in, no import.
`math.sqrt(x)`	Square root.
`min(a, b)`	The smaller of two numbers. Built-in, no import.
`max(a, b)`	The larger of two numbers. Built-in, no import.
`math.pi`	The constant `3.1415...` (a value, not a function).

Call them like any other function:

import math

print(math.floor(3.7))    # 3
print(math.ceil(3.2))     # 4
print(math.sqrt(16))      # 4.0
print(min(7, 3))          # 3
print(math.pi)            # 3.141592653589793

abs(), min(), and max() are built into Python and always available. math.floor, math.ceil, math.sqrt, and math.pi require import math at the top of the file.

Random numbers

Random numbers live in the random module. Import it at the top:

import random

random.random() returns a float between 0.0 and 1.0.
random.randint(a, b) returns a whole number from a to b, both ends included. random.randint(1, 6) is a six-sided die.

import random

print(random.random())          # e.g. 0.6238...
print(random.randint(1, 6))     # e.g. 4
print(random.randint(1, 100))   # e.g. 73

random.randint(a, b) includes both a and b in the possible results. This matches the expected behaviour for dice rolls and similar uses.

Turning text into a number

When a value arrives as a string but you need to do maths with it, use int() for a whole number or float() for a decimal:

text = "42"
n = int(text)
print(n + 1)            # 43

decimal_text = "3.14"
x = float(decimal_text)
print(x * 2)            # 6.28

If the text cannot become a number, Python raises a ValueError:

int("hello")   # ValueError: invalid literal for int()

You will use these conversions a lot in the next chapter, where the program reads keyboard input. Whatever the user types arrives as a string, even if they typed digits.

Homework

Problem 1 — Rectangle area

Open exercises/13/homework/01-rectangle-area.py. Two variables hold a rectangle's width and height. Compute the area and print it with a label, for example Area: 24.

Problem 2 — Floor and ceil

Open exercises/13/homework/02-floor-and-ceil.py. A variable holds the float 3.7. Print it as-is, after math.floor, and after math.ceil. Add one comment line explaining the difference between floor and ceil.

Problem 3 — Roll two dice

Open exercises/13/homework/03-roll-two-dice.py. "Roll" two six-sided dice and print the results like this:

Die 1: 4
Die 2: 6
Total: 10

Use random.randint for the rolls. Roll each die separately so the two values are independent.

Challenge — Hypotenuse

Open exercises/13/homework/04-hypotenuse.py. Two variables hold the two short sides of a right triangle (a and b). Compute and print the hypotenuse c using the Pythagorean theorem:

c = sqrt(a**2 + b**2)

Print all three values labelled. Round the hypotenuse to two decimal places with an f-string and the :.2f format spec from chapter 12.

Stuck or finished? Open the homework solutions page.