Python Numbers: int, float and Math Operators

Integers and Floats

Python has two main kinds of numbers. You met them in chapter 4; now let's see how they behave.

1234score = 100
price = 19.99
print(type(score))
print(type(price))

Think of an int as counting things you can't split, like people or goals, and a float as measuring things you can, like weight or money.

Mixing them

When you combine an int and a float, the answer is a float:

12print(2 + 0.5)
print(3 * 1.0)

3 * 1.0 is a whole amount, but because one side was a float, the result is 3.0.

Big numbers and underscores

For long numbers, you can use _ to make them easier to read. Python ignores it:

12population = 1_400_000_000
print(population)

Floats are not always exact

Computers store floats in a way that can't hold every decimal exactly:

1print(0.1 + 0.2)

This surprises everyone the first time! It's not a bug in Python; almost every programming language does it. You'll learn how to round the result in the last lesson of this topic.

Whole numbers are int, decimal numbers are float. Mix them, and you get a float.

Math Operators

Python's maths symbols are called operators. You know the first four from chapter 2. Here are all seven:

1234print(7 / 2)
print(7 // 2)
print(7 % 2)
print(7 ** 2)

The three new ones

• // divides and throws away the decimal part: 7 // 2 is 3.
• % gives what's left over after dividing: 7 sweets shared by 2 friends leaves 1 sweet. So 7 % 2 is 1.
• ** means "to the power of": 7 ** 2 is 7 times 7.

Think of // and % as a pair: // says how many fit, % says how many are left.

/ always gives a float

1print(6 / 2)

Even when the answer is a whole number, / returns a float. Use // when you want a whole number.

Dividing by zero

1print(5 / 0)

Just like in maths, you can't divide by zero.

// counts how many fit, % gives what's left, ** raises to a power.

The Order of Operations

What does 2 + 3 * 4 give? In Python, as in maths, multiplication comes first:

12print(2 + 3 * 4)
print((2 + 3) * 4)

Without brackets: 3 * 4 is 12, plus 2 makes 14. With brackets: 2 + 3 is 5, times 4 makes 20.

The order Python follows

1. Brackets ( ) first.
2. Powers **.
3. Multiply and divide: *, /, //, %, from left to right.
4. Add and subtract: +, -, from left to right.

You may know this from school as BODMAS, BIDMAS or PEMDAS. Python uses the same idea.

Use brackets to be clear

Even when you don't need them, brackets make your intention obvious:

1234marks = 80
bonus = 10
total = (marks + bonus) * 2
print(total)

A reader sees straight away that the bonus is added before doubling.

A real example: the average

12345a = 70
b = 80
c = 90
print((a + b + c) / 3)
print(a + b + c / 3)

The second line is a classic bug: only c is divided by 3. Brackets fix it.

Brackets first, then powers, then * and /, then + and -.

Shortcuts: +=, -= and More

In chapter 4 you updated a variable with its own value: score = score + 5. That's so common that Python has a shortcut:

123score = 10
score += 5
print(score)

score += 5 means exactly the same as score = score + 5. Read it as "add 5 to score".

The whole family

123456lives = 3
lives -= 1
print("Lives left:", lives)
coins = 50
coins *= 2
print("Coins:", coins)

Think of a scoreboard: you don't rewrite the whole board each time, you just add or take away points.

It works with strings too

+= with a string adds text to the end:

123message = "Hello"
message += ", Sunny!"
print(message)

The variable must exist first

+= uses the old value, so there must be one:

1total += 10

Create it first, for example total = 0, then add to it. You'll use this pattern a lot in the loop chapters, to count and to add up totals.

x += 5 is short for x = x + 5. The variable must already have a value.

Rounding Numbers with round()

Long decimals are hard to read. The built-in round() function tidies them up. Give it the number and how many decimal places you want:

123pi = 3.14159
print(round(pi, 2))
print(round(pi))

• round(pi, 2) keeps two digits after the point: 3.14.
• round(pi), with no second number, rounds to the nearest whole number: 3, an int.

Fixing the 0.1 + 0.2 surprise

Remember 0.30000000000000004 from the first lesson? round() fixes the display:

1print(round(0.1 + 0.2, 2))

round() vs :.2f

You saw :.2f in f-strings. They're related, but not the same:

For money on screen, use :.2f, so it always shows 4.50. For calculations, use round().

A surprise with halves

12print(round(2.5))
print(round(3.5))

When a number is exactly halfway, Python rounds to the nearest even number. It's called "banker's rounding", and it keeps totals fair when you round many numbers. You rarely need to worry about it, but now it won't surprise you.

round(x, 2) keeps two decimal places; round(x) gives the nearest whole number.

Practice: Numbers

Solve these to lock in what you learned in this topic. Each one runs in your browser.

1. 37.Python Program to Find the Quotient and RemainderEasySolve
2. 38.Python Program to Calculate Simple InterestMediumSolve
3. 39.Python Program to Convert Minutes to Hours and MinutesMediumSolve