Lesson 5: Numbers and Arithmetic

What you'll learn in this lesson

• The two kinds of numbers: integers and floats
• The arithmetic operators: add, subtract, multiply, divide
• Whole-number division and remainders
• Powers, and the order Python does operations in
• What happens when you mix text and numbers

Integers and floats

Python has two kinds of numbers:

• An integer (called int) is a whole number: 3, 42, -7.
• A float (called float) is a number with a decimal point: 3.5, 0.25, -1.75. The name comes from "floating point", which is just how computers store decimal numbers.

Python tells them apart by the decimal point. 7 is an integer; 7.0 is a float, even though they represent the same amount. That matters because division always gives you a float, as you will see below.

The basic operators

Try them together:

print(4 + 3)
print(10 - 4)
print(6 * 7)
print(7 / 2)

Output:

7
6
42
3.5

Note that 7 / 2 gives 3.5, not 3. Division in Python always produces a float, even when the answer looks whole: 8 / 2 gives 4.0, not 4.

Whole-number division and remainders

Sometimes you want the whole-number part of a division, or the leftover. Python has two operators for that:

print(7 // 2)
print(7 % 2)
print(8 % 2)

Output:

3
1
0

7 // 2 is 3 (how many whole 2s fit in 7), 7 % 2 is 1 (what is left over), and 8 % 2 is 0 (nothing left over). The // operator is called floor division, and % is the modulo (remainder) operator. Modulo is surprisingly useful: x % 2 tells you whether a number is even (remainder 0) or odd (remainder 1), which you will use in the guessing game and beyond.

Powers, and the order of operations

** raises a number to a power:

print(2 ** 3)
print(5 ** 2)

Output:

8
25

When several operators appear in one line, Python follows the same order you learned in maths — powers first, then multiplication and division, then addition and subtraction. Brackets override everything:

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

Output:

14
20

The first line is 2 + 12 = 14, because 3 * 4 happens first. The second is 5 * 4 = 20, because the brackets force the addition first. When in doubt, add brackets — they make your intention obvious to anyone reading the code, including future you.

Text and numbers do not mix

This is the most common arithmetic surprise for beginners:

print("5" + "3")
print(5 + 3)

Output:

53
8

"5" + "3" joins two pieces of text into "53" — that is called concatenation, and you will meet it properly in Lesson 6. 5 + 3 adds two numbers and gives 8. Same symbols, different result, because quotes change what a value is. If your arithmetic ever gives a strange-looking answer, check whether one of your values is secretly text in quotes.

Hands-on exercise

1. In the shell, work out: 15 + 27, 100 - 38, 9 * 8, 20 / 4. Write down each result and note which ones are floats.
2. Use // and % to split 17 cookies between 5 friends: how many whole cookies each, and how many left over?
3. Predict the result of (10 + 2) * 3 before running it, then check.
4. Try print("4" * 3) in the shell. What happens, and why do you think it happens? (Hint: think about what * does to text.)

Quick quiz

1. What is the difference between an integer and a float?
2. What does 7 / 2 give, and why is it a float?
3. What do // and % compute? Give the results for 9 // 2 and 9 % 2.
4. Why does 2 + 3 * 4 give 14 and not 20?
5. Why does "5" + "3" give 53 while 5 + 3 gives 8?

Answer key: 1. An integer is a whole number; a float has a decimal point. 2. 3.5 — division in Python always produces a float. 3. // is floor (whole-number) division, 9 // 2 = 4; % is the remainder, 9 % 2 = 1. 4. Multiplication happens before addition, so it is 2 + 12. 5. The quoted values are text, so + joins them; the unquoted values are numbers, so + adds them.

Key takeaways

• Integers are whole numbers; floats have decimal points.
• +, -, *, / work as expected, but / always gives a float.
• // gives the whole-number part of a division; % gives the remainder.
• ** is power; brackets override the normal order of operations.
• Quotes change a value's kind: text joins, numbers add.

Next lesson: Strings.

Slides

Work through the slides with Helio's narration, or download them:

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Try it yourself

Run the lesson's example with real Python, right in your browser (Python loads from the internet, so you need to be online).

Open the demo

Practice file

Download lesson05-practice.pyDownload the solution

# Lesson 5: Numbers and Arithmetic
# WHAT TO DO: Share 17 cookies between 5 friends. // (floor division)
# gives whole cookies each, and % (remainder) gives what is left over.
# The "each" line is already right, but one line is wrong. Fix line 13:
# change the leftover from 0 to 17 % 5.
# HINT: 17 shared between 5 friends leaves 2 cookies over, so a correct
# fix prints "Left over: 2".
# Run with F5 in IDLE. You are done when the last line prints 2.

cookies = 17
friends = 5
each = cookies // friends
leftover = 0  # <-- CHANGE THIS LINE: use 17 % 5 (cookies % friends)
print("Each friend gets:")
print(each)
print("Left over:")
print(leftover)

Save the file as lesson05-practice.py and run it with F5 in IDLE. On a Mac, if F5 does nothing, use Run, then Run Module, from the menu.

Check yourself

Five quick questions on this lesson. Take the Lesson 5 quiz