Numbers and the math module

Python distinguishes two fundamental numeric types: int (arbitrary-precision integers — no overflow) and float (64-bit floating point, double precision).

type(42)       # <class 'int'>
type(3.14)     # <class 'float'>
type(10 ** 100)  # <class 'int'>   — interi grandi a piacere

Arithmetic operators

Warning: / always returns a float, even with two integers (10 / 2 returns 5.0, not 5). For integer division use //.

10 / 4    # 2.5
10 // 4   # 2
-7 // 2   # -4   (arrotonda verso il basso, non verso lo zero)

Numeric built-ins

abs(-5)               # 5
min(3, 1, 2)          # 1
max([3, 1, 2])        # 3   (su iterabile)
round(3.7)            # 4
round(3.14159, 2)     # 3.14
sum([1, 2, 3])        # 6

The math module

import math
math.pi               # 3.141592653589793
math.sqrt(16)         # 4.0
math.floor(3.9)       # 3   (verso meno infinito)
math.ceil(3.1)        # 4   (verso più infinito)
math.log(math.e)      # 1.0
math.gcd(12, 18)      # 6

The float pitfall

Floats are binary approximations: 0.1 + 0.2 does not exactly equal 0.3.

0.1 + 0.2           # 0.30000000000000004
0.1 + 0.2 == 0.3    # False !

For safe comparisons use math.isclose(a, b) or, in financial contexts, the decimal module.

Float precision and the decimal module

Floats in Python are implemented as double-precision floating-point numbers (IEEE 754 standard). Consequently, calculations like 0.1 + 0.2 do not yield exactly 0.3, but rather 0.30000000000000004. If you require absolute mathematical precision (e.g. for financial applications), use the standard library's decimal module.

Try it

Review exercise

Additional challenge