Skill: percentages
Fraction–Decimal–Percent Conversions
Percent means “per hundred” — and it is the same number wearing three different outfits. Master the two moves (shift the point; scale the fraction) and you can convert between fractions, decimals, and percents without thinking twice.
1 Understand
The core idea in plain language.
The word percent comes from “per centum” — per hundred. 37% literally means 37/100, which as a decimal is 0.37. One number, three costumes.
Decimal ↔ percent: multiply or divide by 100, which slides the point two places. Decimal → percent slides right (0.4 → 40%); percent → decimal slides left (75% → 0.75).
Fraction ↔ percent: go through the decimal. Divide the numerator by the denominator, then slide right two places: 3/8 = 0.375 = 37.5%. Going back, write the percent over 100 and simplify: 60% = 60/100 = 3/5.
Benchmark percents — 50%, 25%, 10%, 1% — are mental-math shortcuts: half, quarter, a tenth, a hundredth. 10% of 80 is 8, so 20% is 16 and 5% is half of 8, which is 4.
2 See it
Diagrams that make the idea visual.
The conversion triangle
Every conversion is one of two moves: slide the point two places (decimal ↔ percent) or divide / simplify (fraction ↔ the other two).
Memorize the direction: decimal → percent slides right (the number grows: 0.4 → 40). Percent → decimal slides left (40% → 0.4).
Benchmark percents on a 10×10 grid
Fifty percent is half the grid, 25% is a quarter, 10% is one full row, 1% is a single square.
Chain them: 15% of 80 = 10% of 80 (8) + 5% of 80 (half of 8 = 4) = 12.
3 The key rule
Convert the percent to a decimal first, then multiply. 15% of 80 = 0.15 × 80 = 12. Never multiply by the percent number directly.
4 Worked examples
Follow each step. The pattern is always the same.
- Percent means per hundred — multiply by 100.
- Multiplying by 100 slides the point two places right.
- 0.4 → 4.0 → 40, so 0.4 = 40%.
Check: Reverse it: 40% → slide left two → 0.40 = 0.4. Correct.
- Divide first: 3 ÷ 8 = 0.375.
- Slide the point two places right: 0.375 → 37.5.
Check: 37.5% is between 25% (2/8) and 50% (4/8) — 3/8 sits exactly there. Correct.
- Write over 100: 60% = 60/100.
- Simplify by dividing top and bottom by 20: 3/5.
Check: 3/5 = 0.6 = 60%. Correct.
- Convert first: 15% = 0.15.
- Multiply: 0.15 × 80 = 12.
Check: Benchmarks: 10% of 80 is 8, 5% is 4, and 8 + 4 = 12. Correct.
5 Common mistakes
These errors show up on almost every quiz. Spot them now and they will never cost you points.
0.4 = 4% — “I moved the point.”
Decimal → percent slides right: 0.4 = 40%.
15% of 80 = 15 × 80 = 1200.
Convert first: 15% = 0.15, then 0.15 × 80 = 12.
60% = 60/100 — left unsimplified.
Always reduce: 60/100 = 3/5.
6 Key vocabulary
Say these words like you mean them.
- Percent
- Per hundred. 37% = 37/100 = 0.37.
- Benchmark percents
- 50%, 25%, 10%, 1% — easy mental-math anchors.
- Convert
- Rewrite the same value in a different form.
- Simplify
- Divide numerator and denominator by their greatest common factor.
- Per hundred
- The meaning of the % symbol: divide by 100.
- Terminating decimal
- A decimal that ends, like 0.375 — the kind fractions like 3/8 produce.
7 Quick check
Try each one on paper first, then reveal the answer.
Slide right two: 12.5%.
Slide left two: 0.08.
50/200 = 0.25 = 25%.
45/100 simplifies (÷5) to 9/20.
Key points to remember
- Percent = per hundred: p% = p/100.
- Decimal → percent: slide the point right two places. Percent → decimal: slide left.
- Fraction → percent: divide, then slide right two. Percent → fraction: write over 100 and simplify.
- p% of N = (p/100) × N — convert before you multiply.
- Benchmarks: 50% = half, 25% = quarter, 10% = tenth, 1% = hundredth. Chain them for mental math.
- If a percent looks smaller than its decimal, you slid the point the wrong way.