Converting between Fractions, Decimals & Percentages (SQA National 5 Applications of Mathematics): Revision Note

Converting between fractions, decimals & percentages

How do I convert from a percentage to a decimal?

• Divide by 100 (move digits two places to the right)

  • 6% as a decimal is 6 ÷ 100 = 0.06

  • 40% as a decimal is 40 ÷ 100 = 0.4

  • 350% as a decimal is 350 ÷ 100 = 3.5

  • 0.2% as a decimal is 0.2 ÷ 100 = 0.002

How do I convert from a decimal to a percentage?

• Multiply by 100 (move digits two places to the left and add a % sign)

  • 0.35 as a percentage is  0.35 × 100 = 35%

  • 1.32 as a percentage is 1.32 × 100 = 132%

  • 0.004 as a percentage is 0.004 × 100 = 0.4%

How do I convert from a decimal to a fraction?

• If it has one decimal place, write the digits over 10

  • 0.3 is $\frac{3}{10}$

  • 1.1 is $\frac{11}{10}$

• If it has two decimal places, write the digits over 100

  • 0.07 is $\frac{7}{100}$

  • 0.13 is  $\frac{13}{100}$

  • 30.01 is  $\frac{3001}{100}$

• The pattern continues between the number of decimal places and the number of zeroes on the denominator

  • 0.513 is $\frac{513}{1000}$

  • 0.0007 is  $\frac{7}{10000}$

• Whole numbers can be written as fractions by writing them over 1

  • 5 is $\frac{5}{1}$

How do I convert from a percentage to a fraction?

• Write the percentage over 100

  • 37% is $\frac{37}{100}$

How do I convert from a fraction to a decimal?

• Fractions written over powers of 10 are quicker

  • $\frac{3}{5}=\frac{6}{10}$ which is 0.6

  • $\frac{7}{20}=\frac{35}{100}$ which is 0.35

  • $\frac{1}{500}=\frac{2}{1000}$ which is 0.002

• You should be familiar with some basic fractions

How do I convert from a fraction to a percentage?

• If the denominator is 100 then the numerator is the percentage

  • $\frac{17}{100}=17\%$

• Otherwise, change fractions into decimals then multiply by 100

  • $\frac{4}{5}=\frac{8}{10}$ which is 0.8 as a decimal, which is 0.8 × 100 = 80%