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.

Recipe

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:

Financial calculations requiring exact decimal semantics
Scientific computing with floats and tolerances
Bitwise flags and integer protocols
Truth testing in if and while conditions

Working Example

from 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 artifacts
quantize controls rounding for currency display
Fraction keeps rational numbers exact
Truthiness follows standard rules: zero, empty, and None are falsy

Deep Dive

How It Works

int - Arbitrary precision; only limited by memory.
float - IEEE 754 double; fast but inexact for many decimals.
Decimal - Base-10 floating point with configurable precision and rounding modes.
bool - Subclass of int; True == 1, False == 0.
Operator precedence - Standard PEMDAS; use parentheses for clarity.

Operators at a Glance

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

Python Notes

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 itself

Gotchas

Float equality - 0.1 + 0.2 == 0.3 is False. Fix: math.isclose or Decimal.
Floor division on negatives - -7 // 3 is -3, not -2. Fix: Remember floor toward -inf.
Decimal from float - Decimal(0.1) inherits float imprecision. Fix: Decimal("0.1").
bool is int - True + True equals 2. Fix: Do not use bools in sums unless intentional.
Large int to float - Converting huge ints to float loses precision. Fix: Stay in int or use Decimal.

Alternatives

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

FAQs

Why does 0.1 + 0.2 not equal 0.3?

Binary floats cannot represent 0.1 exactly. The sum is close but not identical - use isclose or Decimal.

When should I use Decimal vs float?

Decimal for currency and anywhere humans expect base-10 rounding. float for science, ML, and performance.

What is truthiness?

Objects define truth via __bool__ or __len__. Empty containers and zero numbers are falsy; most other objects are truthy.

How do I round for display?

from decimal import Decimal, ROUND_HALF_UP
Decimal("2.675").quantize(Decimal("0.01"), rounding=ROUND_HALF_UP)

What does // do with negative numbers?

It floors: -7 // 3 is -3 because floor(-2.33) is -3.

Is bool a real integer?

bool subclasses int. isinstance(True, int) is True, but use bools only for logic, not counting.

How do I parse user numeric input safely?

Wrap int() / Decimal() in try/except ValueError, or validate with a schema library at API boundaries.

What is divmod for?

Returns (a // b, a % b) in one call - common for paging and clock arithmetic.

Can ints be infinitely large?

Yes in Python 3 - practical limit is memory. Crypto and bigint math rely on this.

How do bitwise operators work?

They operate on integer bit patterns - useful for flags, masks, and low-level protocols.

Variables, Types & Dynamic Typing - object types and identity
Control Flow - truthiness in conditionals
Strings & f-strings - formatting numbers in output
Type Hints Basics - annotating numeric types

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+.

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.

Recipe

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:

Financial calculations requiring exact decimal semantics
Scientific computing with floats and tolerances
Bitwise flags and integer protocols
Truth testing in if and while conditions

Working Example

from 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 artifacts
quantize controls rounding for currency display
Fraction keeps rational numbers exact
Truthiness follows standard rules: zero, empty, and None are falsy

Deep Dive

How It Works

int - Arbitrary precision; only limited by memory.
float - IEEE 754 double; fast but inexact for many decimals.
Decimal - Base-10 floating point with configurable precision and rounding modes.
bool - Subclass of int; True == 1, False == 0.
Operator precedence - Standard PEMDAS; use parentheses for clarity.

Operators at a Glance

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

Python Notes

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 itself

Gotchas

Float equality - 0.1 + 0.2 == 0.3 is False. Fix: math.isclose or Decimal.
Floor division on negatives - -7 // 3 is -3, not -2. Fix: Remember floor toward -inf.
Decimal from float - Decimal(0.1) inherits float imprecision. Fix: Decimal("0.1").
bool is int - True + True equals 2. Fix: Do not use bools in sums unless intentional.
Large int to float - Converting huge ints to float loses precision. Fix: Stay in int or use Decimal.

Alternatives

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

FAQs

Why does 0.1 + 0.2 not equal 0.3?

Binary floats cannot represent 0.1 exactly. The sum is close but not identical - use isclose or Decimal.

When should I use Decimal vs float?

Decimal for currency and anywhere humans expect base-10 rounding. float for science, ML, and performance.

What is truthiness?

Objects define truth via __bool__ or __len__. Empty containers and zero numbers are falsy; most other objects are truthy.

How do I round for display?

from decimal import Decimal, ROUND_HALF_UP
Decimal("2.675").quantize(Decimal("0.01"), rounding=ROUND_HALF_UP)

What does // do with negative numbers?

It floors: -7 // 3 is -3 because floor(-2.33) is -3.

Is bool a real integer?

bool subclasses int. isinstance(True, int) is True, but use bools only for logic, not counting.

How do I parse user numeric input safely?

Wrap int() / Decimal() in try/except ValueError, or validate with a schema library at API boundaries.

What is divmod for?

Returns (a // b, a % b) in one call - common for paging and clock arithmetic.

Can ints be infinitely large?

Yes in Python 3 - practical limit is memory. Crypto and bigint math rely on this.

How do bitwise operators work?

They operate on integer bit patterns - useful for flags, masks, and low-level protocols.

Variables, Types & Dynamic Typing - object types and identity
Control Flow - truthiness in conditionals
Strings & f-strings - formatting numbers in output
Type Hints Basics - annotating numeric types

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+.

Numbers, Booleans & Arithmetic

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Numbers, Booleans & Arithmetic