Percent to Fraction — the 80/20
x% equals x/100. Remove any decimals, then simplify. The calculator does this exactly and shows the steps.
How it works
- Write x% as x/100.
- If x has decimals, multiply top and bottom by 10^d to clear them.
- Find gcd(n, d) and divide to simplify.
- If improper, optionally express as a mixed number.
Sanity checks
- 50% → 1/2, 25% → 1/4, 75% → 3/4.
- 0% → 0; 100% → 1.
- Decimal check: fraction × 100% should return the original percent.
Shortcuts
- Ends in .5% → denominator 200 (e.g., 12.5% → 1/8).
- Common pairs: 20% = 1/5, 40% = 2/5, 62.5% = 5/8.
- Repeating 33.33…% = 1/3; 66.66…% = 2/3.
Pitfalls
- Forgetting to clear decimals before simplifying.
- Confusing percentage points with percent change.
- Dropping the negative sign for negative percentages.
Micro‑examples
- 12.5% → 12.5/100 → 125/1000 → 1/8.
- 150% → 150/100 = 3/2 = 1 1/2.
- 0.5% → 0.5/100 = 1/200.
Mini‑FAQ
- Improper result? Keep as improper or show as mixed number.
- Decimals okay? Yes—use powers of 10 to clear them.
- Negative values? Apply the sign to the fraction.
Action tip
Type a percent and hit convert—the tool returns the simplified fraction, decimal check, and mixed number if you choose.