Fractions, decimals and percentages · Grade 8

In Grade 8 you learn: recurring decimals.

Fractions, decimals and percentages are three ways of writing the same amount: 1/4 = 0.25 = 25%. Switching between them lets you pick the easiest form for a calculation and compare amounts written in different ways.

Key facts

  • Percentage → decimal: ÷ 100 (35% = 0.35). Decimal → percentage: × 100.
  • Percentage → fraction: write it over 100 and simplify (35% = 35/100 = 7/20).
  • Fraction → decimal: divide the top by the bottom, or make the bottom 10, 100 or 1,000.
  • Learn these: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 1/5 = 0.2 = 20%, 1/8 = 0.125 = 12.5%, 1/3 = 0.333… ≈ 33.3%.
  • To order a mixed list, change everything into decimals (or everything into percentages).
  • More than one whole is more than 100%: 1.35 = 135%.

Worked examples

Example 1

Write 7/20 as a decimal and as a percentage.

Answer: 0.35 and 35%

Example 2

Write 0.45 as a fraction in its simplest form.

Answer: 9/20

Example 3

Put these in order, smallest first: 5/8, 0.6, 63%

Answer: 0.6, 5/8, 63%

Example 4

In a class, 1/4 of the students walk to school, 0.35 cycle and 30% come by bus. The rest come by car. What percentage come by car?

Answer: 10%

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