Converting Between Fractions, Decimals, and Percentages — Practice and Steps for a 12-year-old

Step-by-step guide and practice for a 12-year-old to convert between fractions, decimals, and percentages. Clear rules, worked examples, tips, and practice problems with answers.

PDF

Converting Between Fractions, Decimals, and Percentages (for a 12-year-old)

Here are simple rules and steps with examples so you can convert easily between fractions, decimals, and percentages.

Quick Rules

  • Fraction → Decimal: divide numerator by denominator (top ÷ bottom).
  • Decimal → Fraction: write the decimal as a number over a power of 10 (like 10, 100, 1000) and then simplify.
  • Decimal → Percentage: multiply by 100 (or move the decimal point 2 places to the right) and add a % sign.
  • Percentage → Decimal: divide by 100 (or move the decimal point 2 places to the left) and remove the % sign.
  • Fraction → Percentage: convert the fraction to a decimal then to a percentage, or multiply the fraction by 100% directly.
  • Percentage → Fraction: write the percent over 100 and simplify (like 25% = 25/100 = 1/4).

Worked Examples

1) Fraction → Decimal → Percentage

Example: 3/4

  1. Fraction → Decimal: 3 ÷ 4 = 0.75
  2. Decimal → Percentage: 0.75 × 100 = 75 → 75%
  3. So 3/4 = 0.75 = 75%.

2) Decimal → Fraction → Percentage

Example: 0.6

  1. Decimal → Fraction: 0.6 = 6/10. Simplify 6/10 = 3/5.
  2. Decimal → Percentage: 0.6 × 100 = 60 → 60%.
  3. So 0.6 = 3/5 = 60%.

3) Percentage → Decimal → Fraction

Example: 45%

  1. Percentage → Decimal: 45% = 45 ÷ 100 = 0.45.
  2. Decimal → Fraction: 0.45 = 45/100. Simplify by dividing by 5 → 9/20.
  3. So 45% = 0.45 = 9/20.

More Examples (with short steps)

  • 2/5 → decimal: 2 ÷ 5 = 0.4 → percent: 40%.
  • 7/8 → decimal: 7 ÷ 8 = 0.875 → percent: 87.5%.
  • 0.125 → fraction: 0.125 = 125/1000 = 1/8 → percent: 12.5%.
  • 12.5% → decimal: 0.125 → fraction: 1/8.

Tips

  • If the decimal has 1 digit after the point (like 0.7), use 10 as the denominator (0.7 = 7/10). If it has 2 digits (0.75), use 100 → 75/100. Then simplify.
  • To turn a percent into a fraction, put the number over 100 (percent means "per 100").
  • To go fast between decimals and percentages, move the decimal point two places: right to get percent, left to get decimal.
  • Some decimals repeat (like 0.333...). These can become fractions (0.333... = 1/3). You don't need to worry about repeating decimals yet unless your teacher asks.

Practice Problems (try these first, then check answers)

  1. Convert 5/8 to a decimal and a percent.
  2. Convert 0.45 to a fraction and a percent.
  3. Convert 22% to a decimal and a fraction.
  4. Convert 3/2 to a decimal and a percent.
  5. Convert 0.02 to a fraction and a percent.
  6. Convert 125% to a decimal and a fraction.
  7. Convert 9/25 to a decimal and a percent.
  8. Convert 0.333... (repeating) to a fraction and percent (rounded to 1 decimal place).
  9. Convert 7.5% to a decimal and a fraction.
  10. Convert 4/5 to a decimal and a percent.

Answers (check your work)

  1. 5/8 = 0.625 → 62.5%
  2. 0.45 = 45/100 = 9/20 → 45%
  3. 22% = 0.22 → 22/100 = 11/50
  4. 3/2 = 1.5 → 150%
  5. 0.02 = 2/100 = 1/50 → 2%
  6. 125% = 1.25 → 125/100 = 5/4
  7. 9/25 = 0.36 → 36%
  8. 0.333... = 1/3. As percent ≈ 33.3% (rounded to 1 decimal place)
  9. 7.5% = 0.075 → 7.5/100 = 15/200 = 3/40
  10. 4/5 = 0.8 → 80%

If you want, try more problems and I can check them or show how to do any step in more detail.

Ask a followup question