Lesson 2: Numbers and the math Module

For anything beyond + - * /, import the math module: import math. It works on numbers only and gives fast, accurate results.

Rounding

math.floor(x) and math.ceil(x)

floor rounds down to a whole number, ceil rounds up. Careful with negatives.

import math
print(math.floor(3.7), math.ceil(3.2))
print(math.floor(-3.2), math.ceil(-3.7))

Output:

3 4
-4 -3

math.trunc(x)

Cuts off the decimals (rounds toward zero).

import math
print(math.trunc(3.9), math.trunc(-3.9))

Output:

3 -3

Powers, roots and logs

math.sqrt(x)

The square root. Use math.isqrt(n) for the exact whole-number part.

import math
print(math.sqrt(144))
print(math.isqrt(50))

Output:

12.0
7

math.pow(a, b), math.exp(x)

math.pow always returns a float. exp(x) is e to the power x.

import math
print(math.pow(2, 3))
print(round(math.exp(1), 4))

Output:

8.0
2.7183

math.log(x, base), log2, log10

Logarithms. With one argument it is the natural logarithm.

import math
print(math.log10(1000))
print(math.log2(8))
print(math.log(81, 3))

Output:

3.0
3.0
4.0

Whole-number helpers

math.gcd(a, b) and math.lcm(a, b)

Greatest common divisor and least common multiple.

import math
print(math.gcd(12, 18))
print(math.lcm(4, 6))

Output:

6
12

math.factorial(n)

n! = 1 x 2 x ... x n.

import math
print(math.factorial(5))
print(math.factorial(10))

Output:

120
3628800

math.comb(n, k) and math.perm(n, k)

Combinations (order does not matter) and permutations (order matters).

import math
print(math.comb(5, 2))
print(math.perm(5, 2))

Output:

10
20

Constants and trigonometry

math.pi, math.e, math.inf

Useful constants.

import math
print(round(math.pi, 5))
print(round(math.e, 5))
print(math.inf > 10 ** 100)

Output:

3.14159
2.71828
True

math.sin, cos, tan, radians, degrees

Trigonometry works in radians. Convert with radians() and degrees().

import math
print(round(math.sin(math.radians(30)), 3))
print(round(math.degrees(math.pi), 1))

Output:

0.5
180.0

math.hypot(a, b)

The length of the hypotenuse: sqrt(a squared + b squared).

import math
print(math.hypot(3, 4))

Output:

5.0

Comparing decimals safely

Decimal fractions are stored approximately, so never compare floats with ==. Use math.isclose.

math.isclose(a, b)

True if two floats are equal within a small tolerance.

import math
print(0.1 + 0.2 == 0.3)
print(math.isclose(0.1 + 0.2, 0.3))

Output:

False
True

Number bases

bin(n), oct(n), hex(n) and int(text, base)

Show a number in binary, octal or hexadecimal, and convert text in any base back to an integer.

print(bin(10))
print(oct(64))
print(hex(255))
print(int("1010", 2))
print(int("ff", 16))

Output:

0b1010
0o100
0xff
10
255

random.randint, random.choice, random.random

Random numbers. The results change on every run, so this example is shown but not run. random.seed(n) makes a sequence repeatable.

import random
print(random.randint(1, 6))      # a whole number from 1 to 6
print(random.choice(["a", "b", "c"]))
print(random.random())           # a decimal from 0 up to 1

Try it yourself

1. Calculate the area of a circle of radius 7 with math.pi.
2. Find the gcd and lcm of 84 and 36.
3. How many ways can you choose 3 students from 10? Use math.comb.

Next lesson: text, part one (cleaning and changing).