Using Decimal Arithmetic

Python
from decimal import Decimal, getcontext, ROUND_HALF_UP

# Create Decimals from strings (not floats!) for exactness
price = Decimal("19.99")
tax_rate = Decimal("0.075")

tax = (price * tax_rate).quantize(Decimal("0.01"), rounding=ROUND_HALF_UP)
total = price + tax

print(total)  # Decimal('21.49')

# Compare: float arithmetic introduces error
print(0.1 + 0.2)          # 0.30000000000000004
print(Decimal("0.1") + Decimal("0.2"))  # 0.3

Progress:

• Step 1: Identify why float is insufficient (money, exact decimal rules, auditability)
• Step 2: Construct Decimals from strings or integers, never from floats directly
• Step 3: Set global context precision if defaults (28 digits) are insufficient
• Step 4: Perform arithmetic — operators (+, -, *, /) work naturally
• Step 5: Round/quantize results to the desired number of decimal places
• Step 6: Choose an explicit rounding mode matching business/legal requirements
• Step 7: Handle exceptional conditions (DivisionByZero, InvalidOperation, Overflow) if inputs are untrusted
• Step 8: Use localcontext() for temporary precision/rounding changes scoped to a block

Step 1: Constructing Decimals correctly

Python
# CORRECT — exact
d1 = Decimal("0.1")
d2 = Decimal(10)
d3 = Decimal((0, (3, 1, 4), -2))  # sign, digits tuple, exponent -> 3.14

# WRONG — inherits binary float imprecision
d_bad = Decimal(0.1)  # Decimal('0.1000000000000000055511151231257827021181583404541015625')

Step 2: Setting precision

Python
from decimal import getcontext

getcontext().prec = 50  # global precision (significant digits), default 28

Step 3: Scoped precision with localcontext

Python
from decimal import localcontext

with localcontext() as ctx:
    ctx.prec = 6
    result = Decimal(1) / Decimal(7)  # only affects this block
# outside the block, precision reverts to previous setting

Step 4: Rounding and quantizing

Python
from decimal import (
    ROUND_CEILING, ROUND_FLOOR, ROUND_HALF_UP, ROUND_HALF_EVEN,
    ROUND_DOWN, ROUND_UP, ROUND_05UP
)

value = Decimal("2.675")
value.quantize(Decimal("0.01"), rounding=ROUND_HALF_UP)   # 2.68
value.quantize(Decimal("0.01"), rounding=ROUND_HALF_EVEN)  # 2.67 (banker's rounding, module default)

Step 5: Handling exceptions

Python
from decimal import Decimal, DivisionByZero, InvalidOperation, localcontext

with localcontext() as ctx:
    ctx.traps[DivisionByZero] = True  # raise instead of returning Infinity
    try:
        Decimal(1) / Decimal(0)
    except DivisionByZero:
        print("cannot divide by zero")

Example 1: Currency total with tax Input:

Python
items = [Decimal("12.50"), Decimal("7.25"), Decimal("3.10")]
subtotal = sum(items)
tax = (subtotal * Decimal("0.08")).quantize(Decimal("0.01"), rounding=ROUND_HALF_UP)

Output:

subtotal = Decimal('22.85')
tax = Decimal('1.83')

Example 2: Setting precision for scientific-style computation Input:

Python
from decimal import Decimal, localcontext
with localcontext() as ctx:
    ctx.prec = 10
    result = Decimal(22) / Decimal(7)

Output:

result = Decimal('3.142857143')

Example 3: Comparing Decimal to float safely Input:

Python
Decimal("0.1") == 0.1

Output:

False  # never mix Decimal and float directly in comparisons/arithmetic;
       # convert float via str first: Decimal(str(0.1))