0580

Working with Fractions, Decimals and Percentages

Number

Decimal to fraction

  • The number of decimal places fixes the denominator: one place gives tenths, two gives hundredths, and n places gives 10ⁿ
    • 0.9 is 9/10
    • 0.23 is 23/100
    • 0.041 is 41/1000
  • Write the digits after the point as the numerator, then simplify
    • 0.44 is 44/100, which cancels to 11/25
  • A whole number is written as a fraction by placing it over 1

Percentage to fraction

  • Every percentage is already a number of hundredths, so it goes straight over 100 and is then cancelled
    • 44% is 44/100, which cancels to 11/25

Fraction to decimal

  • Where the denominator divides into a power of ten, scale up to that power and read the decimal straight off
    • 25 goes into 100 four times, so 7/25 becomes 28/100, or 0.28
  • Otherwise divide the numerator by the denominator
  • Denominators that are powers of 2 can be reached by repeated halving
    • 3/8: halving 3 gives 1.5, then 0.75, then 0.375
Common fraction-to-decimal conversions worth recognising on sight, listing a half as 0.5, a fifth as 0.2, a tenth as 0.1, a quarter as 0.25, three quarters as 0.75, a third as 0.3 recurring and two thirds as 0.6 recurring, followed by 5 over 8 set out as a short division of 5.000 by 8 giving 0.625
Source: FDP conversions by Save My Exams

Fraction to percentage

  • Convert to a decimal first, then multiply by 100
    • 9/20 scales to 45/100, which is 0.45, and therefore 45%
Worked example

The four conversions

Write 0.36 as a fraction in its simplest form, and write 3/8 as a decimal and as a percentage.

Solution:

  • 0.36 has two decimal places, so it is 36 hundredths: 0.36 = 36/100
  • Cancel by 4: 36/100 = 9/25
  • For 3/8, divide the numerator by the denominator: 3 ÷ 8 = 0.375
  • To reach a percentage, multiply the decimal by 100: 0.375 × 100 = 37.5%
  • Check the other way round: 37.5 ÷ 100 = 0.375, and 0.375 × 8 = 3