Numbers, Booleans & Arithmetic
Python provides integers of unlimited size, binary floats, and exact numeric types for domains that cannot tolerate rounding error. Booleans participate in arithmetic because they subclass int.
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Python provides integers of unlimited size, binary floats, and exact numeric types for domains that cannot tolerate rounding error. Booleans participate in arithmetic because they subclass int.
from decimal import Decimal
price = Decimal("19.99")
tax = Decimal("0.0825")
total = price * (1 + tax)
a, b = 7, 3
print(a / b, a // b, a % b, divmod(a, b))When to reach for this:
if and while conditionsfrom decimal import Decimal, ROUND_HALF_UP
from fractions import Fraction
def invoice_line(unit_price: str, qty: int, tax_rate: str) -> Decimal:
price = Decimal(unit_price)
tax = Decimal(tax_rate)
subtotal = price * qty
tax_amount = (subtotal * tax).quantize(Decimal("0.01"), rounding=ROUND_HALF_UP)
return subtotal + tax_amount
def float_trap() -> None:
print(0.1 + 0.2) # 0.30000000000000004
print(Fraction(1, 10) + Fraction(2, 10)) # 3/10 exact
def truthiness() -> None:
for value in [0, 1, "", "x", [], [0], None]:
print(repr(value), "->", bool(value))
if __name__ == "__main__":
print(invoice_line("19.99", 3, "0.0825"))
float_trap()
truthiness()What this demonstrates:
Decimal constructed from strings avoids float binary artifactsquantize controls rounding for currency displayFraction keeps rational numbers exactNone are falsyint; True == 1, False == 0.| Operator | Meaning | Notes |
|---|---|---|
/ | True division | Always returns float |
// | Floor division | Rounds toward negative infinity |
% | Modulo | Sign follows divisor in Python 3 |
** | Power | Large ints can grow quickly |
& | ^ << >> | Bitwise | On integers only |
import math
math.isclose(0.1 + 0.2, 0.3) # prefer over == for floats
int("ff", 16) # base conversion
float("nan") != float("nan") # NaN is not equal to itself0.1 + 0.2 == 0.3 is False. Fix: math.isclose or Decimal.-7 // 3 is -3, not -2. Fix: Remember floor toward -inf.Decimal(0.1) inherits float imprecision. Fix: Decimal("0.1").True + True equals 2. Fix: Do not use bools in sums unless intentional.int or use Decimal.| Alternative | Use When | Don't Use When |
|---|---|---|
Decimal | Money, tax, billing | Heavy scientific vector math |
Fraction | Exact rational math | Need transcendental functions |
numpy.float64 | Numeric arrays | Simple script arithmetic |
int only | Counting, indexing | Need fractional values |
Binary floats cannot represent 0.1 exactly. The sum is close but not identical - use isclose or Decimal.
Decimal for currency and anywhere humans expect base-10 rounding. float for science, ML, and performance.
Objects define truth via __bool__ or __len__. Empty containers and zero numbers are falsy; most other objects are truthy.
from decimal import Decimal, ROUND_HALF_UP
Decimal("2.675").quantize(Decimal("0.01"), rounding=ROUND_HALF_UP)It floors: -7 // 3 is -3 because floor(-2.33) is -3.
bool subclasses int. isinstance(True, int) is True, but use bools only for logic, not counting.
Wrap int() / Decimal() in try/except ValueError, or validate with a schema library at API boundaries.
Returns (a // b, a % b) in one call - common for paging and clock arithmetic.
Yes in Python 3 - practical limit is memory. Crypto and bigint math rely on this.
They operate on integer bit patterns - useful for flags, masks, and low-level protocols.
Stack versions: This page was written for Python 3.14.0 (stable 3.14, maintenance 3.13), FastAPI 0.115+, Django 5.2, Flask 3.1, Pydantic 2, PyTorch 2.6+, pandas 2.2+, Polars 1.x, ruff 0.9+, and uv 0.6+.
Reviewed by Chris St. John·Last updated Jul 19, 2026