Python Numbers

3Python Numbers: explained step by step

Python has three built-in kinds of number: int for whole numbers, float for numbers with a decimal point, and complex for numbers with an imaginary part. In everyday programs you will use int and float almost all the time, so this lesson concentrates on them: how they behave, where they surprise you, and how to display them neatly.

Integers have no size limit

An int is a whole number, positive, negative or zero. Unlike many languages, Python integers can be as big as your memory allows, so you never get an overflow. For readability you can put underscores inside a long literal; Python ignores them.

population = 8_100_000_000
print(population)
print(type(population))
print(2 ** 100)

You can also write integers in other bases: 0b1010 is binary, 0o17 is octal and 0xFF is hexadecimal. bin(), oct() and hex() convert the other way.

print(0b1010, 0o17, 0xFF)
print(bin(10), hex(255))

Floats are numbers with a decimal point

A float is any number written with a . or in scientific notation such as 1.5e3 (which means 1.5 x 10^3). Dividing with / always gives a float, even when the answer looks whole. This surprises many beginners, and it matters when you later try to use that value as a count or an index.

print(7 / 2)
print(8 / 2)
print(type(8 / 2))
print(1.5e3, 2e-3)

Mixing an int and a float in one calculation gives a float. Converting between types is covered in Python casting, and the basic types are introduced in Python data types.

Floor division, remainder and divmod

Besides /, there are two operators that work with whole-number division, described in Python operators:

• // is floor division: how many times does it fit, rounded down.
• % is the modulo (remainder): what is left over.

divmod(a, b) returns both at once, which is handy for converting minutes into hours and minutes.

minutes = 135
hours = minutes // 60
left = minutes % 60
print(hours, left)
print(divmod(minutes, 60))
print(-7 // 2, -7 % 2)

Notice that floor division rounds towards minus infinity, so -7 // 2 is -4, not -3. And ** raises to a power: 3 ** 2 is 9.

Built-in helpers: abs, round, min, max and sum

Several functions work on numbers without any import: abs() removes the sign, round() rounds, and min(), max() and sum() work on a list of numbers. More tools live in the math module, covered in Python math and statistics.

temps = [18.5, 21.0, 19.25, 23.5]
print(abs(-12), min(temps), max(temps))
print(sum(temps) / len(temps))
print(round(3.14159, 2), round(2.5), round(3.5))

round() with one argument gives an int. It rounds halves to the nearest even number (called banker's rounding), so round(2.5) is 2 and round(3.5) is 4. This is correct behaviour, not a bug.

Why 0.1 + 0.2 is not exactly 0.3

Computers store floats in binary, and a number like 0.1 cannot be stored exactly, just as 1/3 cannot be written exactly in decimals. The tiny error shows up in the results.

total = 0.1 + 0.2
print(total)
print(total == 0.3)
print(round(total, 2) == 0.3)

So never compare floats with ==. Use round() first, or better, math.isclose(a, b), which checks that two numbers are close enough. For money, where exact cents matter, use the Decimal type or store whole cents as integers.

Formatting numbers with f-strings

Often you only want to display a number nicely. In an f-string, :.2f shows two decimals and :, adds thousands separators. The number itself is not changed. More formatting tricks appear in Python input and output.

price = 1234.5
print(f"Price: {price:.2f}")
print(f"Price: {price:,.2f}")
print(f"Views: {2500000:,}")

Complex numbers in one paragraph

A complex number has a real and an imaginary part, written with a j, like 3 + 4j. They are used in engineering and science and are rare in beginner code. If you need one, abs(3 + 4j) gives its size, 5.0.

Which number type should I use?

• Counts, positions and anything you cannot split: int.
• Measurements and averages: float, and format them when you display them.
• Money: whole cents as int, or Decimal.
• Text that looks like a number, such as "42": it is a string until you convert it.