Fraction → percent in three crisp steps
Core idea
Compute (numerator ÷ denominator) × 100, then format with % and your chosen decimal places; reduce the fraction first for clarity.
How it works
- Simplify a/b → a′/b′ using GCD.
- Decimal = a′/b′; Percent = 100 × Decimal.
- Show exact and rounded forms separately (rounding is display‑only).
Sanity checks
- Back‑convert: percent/100 ≈ decimal value.
- Sign is preserved: negative fractions yield negative percentages.
- 100% corresponds to equal parts (num = den in lowest terms).
Shortcuts
- Denominator 4 → quarters: 1/4=25%, 3/4=75%.
- Fifths: 1/5=20%, 2/5=40%, 3/5=60%, 4/5=80%.
- Eighths: 1/8=12.5%, 3/8=37.5%, 5/8=62.5%, 7/8=87.5%.
Pitfalls
- Multiplying by 100 twice (once in decimal step, again in display).
- Rounding too early in a multi‑step calculation.
- Forgetting to simplify when an exact over‑100 fraction exists.
Micro‑examples
- 3/4 → 0.75 → 75%
- 5/8 → 0.625 → 62.5%
- −7/5 → −1.4 → −140%
Mini‑FAQ
- Can results exceed 100%? Yes—improper fractions map to >100%.
- Exact vs rounded? Both are shown; rounding affects display only.
- Mixed numbers? Convert to improper, then proceed.
Action tip
Enter the fraction, pick decimal places, and compare the “Exact” vs “Rounded” cards to report the right precision for your context.