Numbers

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Python has four built-in numeric types — int, float, complex, and bool — plus two standard-library types, decimal.Decimal and fractions.Fraction, for arithmetic that must avoid binary floating-point error.

int, float, complex, and Numeric Literals

int has arbitrary precision — it grows to fit the value, with no fixed bit width and no silent overflow. float is a 64-bit IEEE 754 double, which means most decimal fractions have no exact binary representation. complex stores a pair of floats as real and imag. All three are documented under Numeric Types — int, float, complex; the tutorial’s Numbers section is a gentler introduction.

big = 2 ** 100                 # int: no overflow, arbitrarily large
pi_ish = 3.14159                # float
z = 2 + 3j                      # complex: real=2.0, imag=3.0

million = 1_000_000             # underscores as visual separators
hex_val = 0x1F                  # 31, hexadecimal
oct_val = 0o17                  # 15, octal
bin_val = 0b1010                # 10, binary
>>> 2 ** 100
1267650600228229401496703205376
>>> 0.1 + 0.2
0.30000000000000004
>>> (2 + 3j).imag
3.0

That last result is not a bug: 0.1 and 0.2 cannot be represented exactly in binary, so their sum carries a tiny error. See Floating Point Arithmetic: Issues and Limitations for why, and the decimal/fractions section below for exact alternatives.

Operators

Arithmetic operators are +, -, , /, //, %, and . / is *true division and always returns a float; // is floor division and rounds toward negative infinity; % is the matching modulo; is exponentiation.

7 / 2        # 3.5   (true division: always float)
7 // 2       # 3     (floor division)
-7 // 2      # -4    (rounds toward -infinity, not toward zero)
7 % 2        # 1
-7 % 2       # 1     (result takes the sign of the divisor)
2 ** 10      # 1024

Comparisons chain: a < b < c means a < b and b < c, evaluating b only once:

x = 5
print(0 < x < 10)     # True
print(10 < x < 20)    # False

Augmented assignment combines an operator with =:

total = 10
total += 5    # 15
total -= 3    # 12
total *= 2    # 24
total //= 5   # 4
total **= 2   # 16

Exact Arithmetic: decimal.Decimal and fractions.Fraction

decimal.Decimal represents numbers in base 10, avoiding the binary rounding error shown above — useful for money and other values with an exact decimal representation. See the decimal module.

from decimal import Decimal

price = Decimal("0.1") + Decimal("0.2")
print(price)             # 0.3  (exact)

fractions.Fraction keeps an exact numerator/denominator pair, so ratios never lose precision either. See the fractions module.

from fractions import Fraction

f = Fraction(1, 3) + Fraction(1, 6)
print(f)                 # 1/2
print(float(f))          # 0.5

bool is an int subclass: True and False behave as 1 and 0 in arithmetic.

print(True + True)       # 2
print(isinstance(True, int))   # True
print(True * 10)         # 10

Built-in Numeric Tools

abs() returns the magnitude, round() rounds to the given number of decimal places, and pow() is exponentiation with an optional modulus. Full reference: Numeric Types — int, float, complex.

abs(-7)          # 7
abs(-3.5)        # 3.5
round(2.5)       # 2   (banker's rounding: ties go to the nearest even int)
round(3.5)       # 4
round(3.14159, 2)  # 3.14
pow(2, 10)       # 1024
pow(2, 10, 1000) # 24  (2 ** 10 % 1000, computed efficiently)

round()’s tie-breaking rule — round half to even, or "banker’s rounding" — avoids the statistical bias of always rounding `.5 up; round(0.5) is 0, and round(1.5) is 2.

The math module supplies everything beyond these basics — square roots, trigonometry, logarithms, constants like math.pi:

import math

math.sqrt(2)      # 1.4142135623730951
math.floor(3.7)   # 3
math.pi           # 3.141592653589793

math (plus random and statistics) is covered in depth in Standard Library Tour.

See Also