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}.

flashcards

Question	Answer
0.5 as a fraction	\frac{1}{2}
0.75 as a fraction	\frac{3}{4}
0.32 as a fraction	\frac{8}{25}
7.125 as a fraction	\frac{57}{8}
0.04 as a fraction	\frac{1}{25}
What type of decimal can be converted by simply using the place value of the last digit?	Only terminating decimals (decimals that come to an end).
How do you write a terminating decimal as a fraction?	Write the decimal digits over the power of 10 indicated by the last digit’s place value (e.g., tenths = denominator 10, hundredths = denominator 100, thousandths = denominator 1000).
After writing a decimal as a fraction over a power of 10, what is the next step?	Simplify the fraction by dividing numerator and denominator by their highest common factor (HCF).
What is the first step to convert 0.5 to a fraction?	The 5 is in the tenths place, so write it as \frac{5}{10}.
What is the HCF of 5 and 10 when simplifying \frac{5}{10}?	The HCF is 5.
How do you simplify 0.5 = \frac{5}{10} fully?	\frac{5 \div 5}{10 \div 5} = \frac{1}{2}.
How do you write 0.75 as an initial fraction?	The 7 is in the tenths place and the 5 is in the hundredths place, so \frac{75}{100}.
What is the HCF of 75 and 100?	The HCF is 25.
How do you simplify 0.75 = \frac{75}{100} fully?	\frac{75 \div 25}{100 \div 25} = \frac{3}{4}.
How do you write 0.32 as an initial fraction?	The 3 is in the tenths place and the 2 is in the hundredths place, so \frac{32}{100}.
What is the HCF of 32 and 100?	The HCF is 4.
How do you simplify 0.32 = \frac{32}{100} fully?	\frac{32 \div 4}{100 \div 4} = \frac{8}{25}.
How do you write 7.125 as an initial fraction?	The 7 is in the units place, and the 1, 2, 5 are in tenths, hundredths, thousandths respectively, so 7\frac{125}{1000} or \frac{7125}{1000}.
What is the HCF of 7125 and 1000?	The HCF is 125.
How do you simplify 7.125 = \frac{7125}{1000} fully?	\frac{7125 \div 125}{1000 \div 125} = \frac{57}{8}.
How do you write 0.04 as an initial fraction?	The 4 is in the hundredths place, so \frac{4}{100}.
What is the HCF of 4 and 100?	The HCF is 4.
How do you simplify 0.04 = \frac{4}{100} fully?	\frac{4 \div 4}{100 \div 4} = \frac{1}{25}.
Why does converting decimals to fractions using place values work?	Because we work with base 10 (decimal) numbers, so it’s easy to convert to fractions where the denominator is a power of 10.
What does 0.1 equal as a fraction and why?	\frac{1}{10} because the 1 is in the tenths place.
What does 0.72 equal as a fraction and why?	\frac{72}{100} because the 7 is in the tenths place and the 2 is in the hundredths place.