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Converting Between Decimals & Fractions

Maths: Year 5 & 6 National Curriculum, topic 1.4.6

Converting Between Simple Fractions and Decimals

One half

One half

  • 12\large\frac{1}{2} is the same as 0.5.
    • 12\large\frac{1}{2} is the same as 0.5 because 1 whole is the same as 100 'hundredths'.
  • 12\large\frac{1}{2} of 100 'hundredths' is 50 'hundredths' which is the same as 0.5.
One quarter

One quarter

  • 14\large\frac{1}{4} is the same as 0.25.
    • 14\large\frac{1}{4} is the same as 0.25 because 1 whole is the same as 100 'hundredths'.
  • 14\large\frac{1}{4} of 100 'hundredths' is 25 'hundredths' which is the same as 0.25.
One fifth

One fifth

  • 15\large\frac{1}{5} is the same as 0.2.
    • 15\large\frac{1}{5} is the same as 0.2 because 1 whole is the same as 100 'hundredths'.
  • 15\large\frac{1}{5} of 100 'hundredths' is 20 'hundredths' which is the same as 0.2.
Two fifths

Two fifths

  • 25\large\frac{2}{5} is 2 lots of 15\large\frac{1}{5}.
  • 15\large\frac{1}{5} = 0.2
  • 25\large\frac{2}{5} = 0.2 × 2 = 0.4
Four fifths

Four fifths

  • 45\large\frac{4}{5} is 4 lots of 15\large\frac{1}{5}.
  • 15\large\frac{1}{5} = 0.2
  • 45\large\frac{4}{5} = 0.2 × 4 = 0.8

Converting Between More Complex Fractions and Decimals

E.g.1 Fraction to decimal

E.g.1 Fraction to decimal

  • 71100\large\frac{71}{100} is the same as 0.71.
  • 71100\large\frac{71}{100} is the same as 0.71 because there are 7 'tenths' and 1 'hundredth' in 0.71.
E.g.1 Fraction to decimal cont.

E.g.1 Fraction to decimal cont.

  • 0.7 can be shown in two ways.
  • There are 7 'tenths' in 0.7 so 0.7 can be shown as 710\large\frac{7}{10}
  • 0.7 is also the same as 70 'hundredths' so can be shown as 70100\large\frac{70}{100}
E.g.2 Decimal to fraction

E.g.2 Decimal to fraction

  • 310\large\frac{3}{10} is the same as 0.3.
  • 310\large\frac{3}{10} can also be shown as 30100\large\frac{30}{100}
E.g.3 Decimal to fraction

E.g.3 Decimal to fraction

  • 0.42 can be shown as 42100\large\frac{42}{100}

Test yourself on Converting Between Decimals & Fractions

  • What is 15\large\frac{1}{5} as a decimal?

  • What is 12\large\frac{1}{2} as a decimal?

  • What is 35\large\frac{3}{5} as a decimal?

  • What is 34\large\frac{3}{4} as a decimal?

  • What is 56100\large\frac{56}{100} as a decimal?

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