The conversion map
There are only six moves, and three of them are the reverse of the others.
- Fraction → decimal: divide the top by the bottom. 3/8 = 3 ÷ 8 = 0.375.
- Decimal → percent: multiply by 100. 0.375 → 37.5%.
- Percent → decimal: divide by 100. 62% → 0.62.
- Decimal → fraction: write over 10, 100 or 1000, then simplify. 0.45 = 45/100 = 9/20.
- Fraction → percent: convert to a decimal first, then ×100. 5/8 = 0.625 = 62.5%.
- Percent → fraction: put it over 100 and simplify. 24% = 24/100 = 6/25.
Worked examples
Convert 7/20 to a percent: 7 ÷ 20 = 0.35, then ×100 = 35%.
Convert 0.08 to a fraction: 8/100 = 2/25.
Convert 135% to a decimal and a fraction: 1.35, and 135/100 = 27/20 = 1 7/20.
Repeating decimals
Some fractions never terminate: 1/3 = 0.333… written as 0.3̄, and 2/3 = 0.666… ≈ 66.7%. Round only at the final step, and only to the precision the question asks for.
Worth memorising
These come up constantly in tests and shopping problems alike: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, 1/8 = 0.125 = 12.5%, 1/3 ≈ 0.333 ≈ 33.3%, 1/10 = 0.1 = 10%.