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Percentages

  • Percentage or per cent means hundredths. ∴ 34% is another way of writing 34/100
  • The symbol ‘%’ is short for per cent.
  • To change a percentage to a fraction, write it as a fraction of 100 and reduce it to its lowest terms, where possible.
  • To change a fraction to a percentage, multiply the fraction by 100.
  • To express a quantity as a percentage of another:
    • make sure they are in the same units,
    • express the first as a fraction of the second,
    • multiply the fraction by 100.
Examples
  1. Express 15% as a fraction in its lowest terms.
    • 15% = 15/100 = 3 × 5/20 × 5 = 3/20
  2. Express 2/5 as a percentage.
    • 2/5 = 2 × 20/5 × 20
    •      = 40/100
    •      = 40%
  3. A worker hammers a post 2.2 m long into the ground. 66 cm of the post is below the ground. What percentage of the post is above the ground?
    • Fraction of post below the ground = 66 cm/2.2 m = 66 cm/220 cm = 66/220
    • Percentage of the post below the ground = 66/220 × 100% = 6/20 × 100 = 30%
    • ∴ Percentage of post above the ground = 100% – 30% = 70%
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