Converting decimals to fractions

Because we work with base 10 (decimal) numbers, it’s very easy for us to convert decimals to fractions where the denominator is a power of 10.

For example, we know that 0.1 is the same as 1/10, because the 1 is in the tenths place. Similarly, 0.72 is the same as 72/100, because the 2 is in the hundredths place and the 7 is in the tenths place.

This only works for terminating decimals, which are decimals that come to an end. See converting recurring decimals to fractions for a method to convert recurring decimals to fractions.

Simplifying

Once we’ve found the decimal as a fraction of a power of 10, we need to simplify it.

To do this, we first need to find the highest common factor. See the link to learn how to find the HCF.

Example conversions

Convert 0.5 to a fraction

• The 5 is in the tenths place, so we can write it as \frac{5}{10}.
• Simplify:
  • The HCF of 5 and 10 is 5.
  • \frac{5 \div 5}{10 \div 5} = \frac{1}{2}.
• Answer: 0.5 = \frac{1}{2}.

Convert 0.75 to a fraction

• The 7 is in the tenths place and the 5 is in the hundredths place, so we can write it as \frac{75}{100}.
• Simplify:
  • The HCF of 75 and 100 is 25.
  • \frac{75 \div 25}{100 \div 25} = \frac{3}{4}.
• Answer: 0.75 = \frac{3}{4}.

Convert 0.32 to a fraction

• The 3 is in the tenths place and the 2 is in the hundredths place, so we can write it as \frac{32}{100}.
• Simplify:
  • The HCF of 32 and 100 is 4.
  • \frac{32 \div 4}{100 \div 4} = \frac{8}{25}.
• Answer: 0.32 = \frac{8}{25}.

Convert 7.125 to a fraction

• The 7 is in the units place, so we start with 7.
• The 1 is in the tenths place, the 2 is in the hundredths place, and the 5 is in the thousandths place, so we can write it as \frac{7125}{1000}.
• Simplify:
  • The HCF of 7125 and 1000 is 125.
  • \frac{7125 \div 125}{1000 \div 125} = \frac{57}{8}.
• Answer: 7.125 = \frac{57}{8}.

Convert 0.04 to a fraction

• The 4 is in the hundredths place, so we can write it as \frac{4}{100}.
• Simplify:
  • The HCF of 4 and 100 is 4.
  • \frac{4 \div 4}{100 \div 4} = \frac{1}{25}.
• Answer: 0.04 = \frac{1}{25}.