Numbers and Math

Python is a great calculator, and that's where most programs start: adding up prices, averaging scores, measuring things. In this lesson you'll learn how Python works with numbers.

Two kinds of numbers

Python has two main number types:

• int: whole numbers, such as 7, -3 and 1000000
• float: numbers with a decimal point, such as 3.14, -0.5 and 2.0

print(type(42))
print(type(42.0))
print(type(-7))
print(type(3.5))

42 and 42.0 are the same amount, but different types: the decimal point makes 42.0 a float.

Write numbers without commas or spaces: 1000000, not 1,000,000. Python reads commas as separators between values, so print(1,000) prints 1 0, two separate numbers.

Arithmetic operators

print(7 + 2)
print(7 - 2)
print(7 * 2)
print(7 / 2)
print(7 // 2)
print(7 % 2)
print(7 ** 2)

Notice that / always gives a float, even when the numbers divide evenly:

print(10 / 2)    # 5.0, not 5
print(10 // 2)   # 5

Dividing by zero is an error with every division operator (/, // and %). Python stops with a ZeroDivisionError:

print(10 / 0)

Whole-number division and remainder

// and % are a pair. Think of sharing sweets: // tells you how many each person gets, and % tells you how many are left over.

sweets = 17
people = 5

print("Each person gets", sweets // people)
print("Left over:", sweets % people)

They're handy for converting units, like minutes into hours:

total_minutes = 135

hours = total_minutes // 60
minutes = total_minutes % 60

print(hours, "hours and", minutes, "minutes")

Here's the working for 17 sweets and 5 people: 5 goes into 17 three whole times (17 // 5 is 3), which uses 15 sweets, and 17 - 15 leaves 2 (17 % 5 is 2).

A common trick: a number is even if number % 2 is 0, because nothing is left over when you divide it by 2.

print(10 % 2)   # 0, so 10 is even
print(7 % 2)    # 1, so 7 is odd

Order of operations

Python follows the same rules as maths. Higher rows in this table happen first:

Operators in the same row are worked out left to right. Use parentheses to change the order, or just to make your intent clear.

Predict first: what will each line print?

print(2 + 3 * 4)
print((2 + 3) * 4)
print(10 - 4 - 3)

• 2 + 3 * 4 is 14: the multiplication 3 * 4 happens first, then 2 + 12.
• (2 + 3) * 4 is 20: the parentheses go first, then 5 * 4.
• 10 - 4 - 3 is 3: both are subtractions, so left to right, (10 - 4) - 3. Not 10 - (4 - 3), which would be 9.

Mixing ints and floats

When you combine an int with a float, the result is a float:

print(3 + 2.0)
print(4 * 0.5)

Floats aren't always exact

Computers store decimal numbers in a way that can't represent every value exactly. This surprises everyone the first time:

print(0.1 + 0.2)

Instead of 0.3, you get 0.30000000000000004. That's not a Python bug; every programming language does this. The error is tiny, so it doesn't matter for most calculations. The fix is simple: round results before showing them to people.

Rounding

round(number) rounds to the nearest whole number, and round(number, digits) keeps that many decimal places:

print(round(3.7))
print(round(3.14159, 2))
print(round(0.1 + 0.2, 2))

round() gives back a new number; it doesn't change a variable unless you store the result, as in price = round(price, 2). It also doesn't add zeros: round(2.5, 2) is still 2.5, not 2.50.

Showing a fixed number of decimals

Prices usually need exactly two decimal places, even when the number is whole. In an f-string, put :.2f after the value inside the braces:

price = 4.5
total = price * 3

print(f"Total: {total}")
print(f"Total: {total:.2f}")
print(f"Pi is about {3.14159:.2f}")

Read .2f as "2 digits after the decimal point". It rounds if there are more digits and adds zeros if there are fewer, so 13.5 shows as 13.50. Use round() when you want to keep calculating with the number, and :.2f when you're showing it to someone. You'll learn more of these formatting codes in the String Formatting lesson.

print(round(0.5))
print(round(1.5))
print(round(2.5))
print(round(3.5))

Updating a variable

You'll often change a variable based on its current value. Python has shortcuts for this:

score = 10
score += 5     # same as score = score + 5
print(score)

score -= 3     # same as score = score - 3
print(score)

score *= 2     # same as score = score * 2
print(score)

Read score += 5 as "add 5 to score". There's a shortcut for each operator:

The variable must already exist. total += 5 on a brand-new name gives a NameError, because there's no current value to add to.

Useful built-in functions

Python has a few maths functions built in, ready to use:

print(abs(-12))          # distance from zero: 12
print(min(4, 9, 1, 7))   # smallest: 1
print(max(4, 9, 1, 7))   # largest: 9

The math module

Python comes with extra toolboxes called modules. The math module has more advanced maths. Write import math once at the top of your program to load it, then use its tools with math. in front. (You'll learn more in the Modules and Imports lesson in Part 4.)

import math

print(math.pi)
print(math.sqrt(16))     # square root
print(math.floor(3.7))   # round down
print(math.ceil(3.2))    # round up

Without the import math line, math.sqrt(16) gives a NameError.

For example, the area of a circle is π × r²:

import math

radius = 5
area = math.pi * radius ** 2
print(f"Area: {area:.2f}")

print(2 ** 100)
print(1_000_000 * 3)

print(pow(2, 5))
print(divmod(17, 5))

print(7 // 2)
print(-7 // 2)

print(2 ** 3 ** 2)
print((2 ** 3) ** 2)

Exercises

Exercise 1: Average of three scores

Calculate and print the average of the three scores, rounded to 1 decimal place. The expected output is 81.7.

score1 = 78
score2 = 92
score3 = 75

Exercise 2: Seconds to minutes

Convert 500 seconds into minutes and seconds using // and %. Print: 8 minutes and 20 seconds.

total_seconds = 500

Exercise 3: Shopping bill

A shirt costs 19.99 and you're buying 3. There's a 10% discount on the total. Print the final price with 2 decimal places: Total: 53.97.

price = 19.99
quantity = 3
discount = 0.10

Exercise 4: Hypotenuse

The hypotenuse of a right triangle is √(a² + b²). Use the math module to calculate it for sides 3 and 4. The answer is 5.0.

a = 3
b = 4

Number tools at a glance

A quick reference for later. The arithmetic operators (+, -, *, /, //, %, **) are in the table near the top of this lesson.

Built-in functions (no import needed)

Converting between types

Updating a variable (each example starts from x = 10)

The math module (write import math first)

Summary

• int holds whole numbers, and float holds numbers with a decimal point.
• / always gives a float. // gives the whole part, and % gives the remainder.
• Python follows the usual order of operations. Use parentheses to be clear.
• Floats can be slightly inexact, so round results before showing them: round(x, 2) or f"{x:.2f}".
• score += 5 is a shortcut for score = score + 5.
• abs, min, max and round are built in. import math gives you sqrt, pi, floor and ceil.