How to Convert Decimals to Fractions Part 1

April 2, 2015 Civil Service Reviewer Mathematics

We have learned how to convert fractions to decimals and in this post, we are going to learn how to convert decimals to fractions. Before doing this, we need to review the meaning of place value. In the decimal number 0.532, 5 is the tenths place, 3 is the hundredths place, 2 is the thousandths place.

The number 5 tenths is the same as $5 \times \frac{1}{10}$ , 3 hundredths is the same as $3 \times \frac{1}{100}$ and 2 thousandths is the same as $2 \times \frac{1}{1000}$ . In converting decimals to fractions, we have to see the place value of the last digit of the decimal place.

Example 1

Convert $0.7$ to fraction.

Solution

0.7 is 7 tenths or $7 \times \frac{1}{10} = \frac{7}{10}$ .

Therefore, the equivalent of $0.7$ in fraction is the same as $\displaystyle \frac{7}{10}$

Example 2

Convert $0.6$ to fraction.

0.6 is $6 \times \displaystyle \frac{1}{10} = \frac{6}{10}$

We reduce the fraction to lowest terms by dividing both the numerator and the denominator by the greatest common factor of 6 and 10 which is 2.

$\displaystyle \frac{6 \div 2}{10 \div 2} = \frac{3}{5}$

Therefore, the equivalent fraction of $0.6$ is $\frac{3}{5}$ .

Example 3

Convert $0.12$ to fraction

The last digit of the decimal is in the hundredths place, so we can read this as 12 hundredths.

Twelve hundredths is $12 \times \displaystyle \frac{1}{100} = \frac{12}{100}$ .

We convert this fraction to lowest terms by dividing both the numerator and denominator by the greatest common factor of 12 and 100 which is equal to 4. So,

$\displaystyle \frac{12 \div 4}{100 \div 4} = \frac{3}{25}$ .

Therefore, the equivalent of 0.12 in fraction is $\displaystyle \frac{3}{25}$

Example 4

Convert $0.375$ to fraction.

Solution

The last digit of the decimal number above is in the thousandths place. So, we can read it as 375 thousandths.

Now, 375 thousandths is the same as $375 \times \displaystyle \frac{1}{1000} = \frac{375}{1000}$ .

We convert 375 thousandths to lowest terms by dividing both its numerator and denominator by the greatest common factor of 375 and 1000 which is equal to 125. That is,

$\displaystyle \frac{375 \div 125}{1000 \div 125} = \frac{3}{8}$ .