Python — Math

Operators recap + extras

10 / 3      # 3.333…  true division (always float)
10 // 3     # 3       floor division
10 % 3      # 1       remainder
2 ** 10     # 1024    power
divmod(10, 3)   # (3, 1)  quotient AND remainder together

divmod shines in time conversions:

h, rem = divmod(7384, 3600)
m, s = divmod(rem, 60)        # 2h 3m 4s

Built-in numeric functions

abs(-7)               # 7
round(3.14159, 2)     # 3.14    round-half-to-EVEN quirk: round(2.5) → 2!
max(3, 7, 5); min(...)
sum([1, 2, 3], start=10)   # 16

That round(2.5) == 2 surprises everyone — banker's rounding. For half-up use int(x + 0.5) on positives or decimal module.

The math module

import math

math.floor(4.9);  math.ceil(4.1)
math.sqrt(81)         # 9.0
math.isqrt(81)        # 9     integer sqrt — exact for big ints!
math.pow(2, 8)        # 256.0
math.factorial(5)     # 120
math.gcd(12, 18)      # 6
math.pi; math.e; math.inf; math.nan

Trig takes RADIANS:

math.sin(math.pi / 2)          # 1.0
math.degrees(math.pi)          # 180
math.radians(90)               # 1.5707…

Logarithms with bases:

math.log(1000)       # natural ln ≈ 6.9
math.log10(1000)     # 3.0
math.log2(8)         # 3.0

Random numbers

import random

random.random()                    # [0.0, 1.0)
random.randint(1, 6)               # inclusive dice
random.uniform(1.5, 3.5)           # float range
random.choice(["a", "b"])          # one item
random.choices(pop, k=3)           # WITH replacement
random.sample(pop, 3)              # WITHOUT replacement — unique picks
random.shuffle(deck)               # in-place shuffle

Reproducibility for tests:

random.seed(42)    # same "random" sequence every run

Security note: tokens need secrets.token_hex(16), not random.

Floating-point precision

0.1 + 0.2 == 0.3          # False 😱
round(0.1 + 0.2, 10) == 0.3    # True

from decimal import Decimal
Decimal("0.1") + Decimal("0.2")    # Decimal('0.3') exact — money-grade

Mini Practice

1. Seconds → "2h 03m 04s" via divmod.
2. Compare round/floor/ceil/trunc on ±values.
3. Dice-roll tally over 600 throws using randint.
4. Sample 5 unique lottery numbers from 1–49.
5. Exact 0.1+0.2 via Decimal.

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