How to Convert from Decimals to Fractions

Some conversions from very common decimals to fractions are easy. In other cases, you have to do a bit more work. Here’s how to change any decimal into a fraction:

1. Create a “fraction” with the decimal in the numerator and 1.0 in the denominator.

   This isn’t really a fraction, because a fraction always has whole numbers in both the numerator and denominator, but you turn it into a fraction in Step 2.

   When converting a decimal that’s greater than 1 to a fraction, separate out the whole-number part of the decimal before you begin; work only with the decimal part. The resulting fraction is a mixed number.

2. Move the decimal point in the numerator enough places to the right to turn the numerator into a whole number, and move the decimal point in the denominator the same number of places.

3. Drop the decimal points and any trailing zeros.

4. Reduce the fraction to lowest terms if necessary.

A quick way to make a fraction out of a decimal is to use the name of the smallest decimal place in that decimal. For example,

• In the decimal 0.3, the smallest decimal place is the tenths place, so the equivalent fraction is

  

• In the decimal 0.29, the smallest decimal place is the hundredths place, so the equivalent fraction is

  

• In the decimal 0.817, the smallest decimal place is the hundredths place, so the equivalent fraction is

  

Sample questions

1. Change the decimal 0.83 to a fraction.

   

   Create a “fraction” with 0.83 in the numerator and 1.0 in the denominator:

   

   Move the decimal point in 0.83 two places to the right to turn it into a whole number; move the decimal point in the denominator the same number of places. Do this one decimal place at a time:

   

   At this point, you can drop the decimal points and trailing zeros in both the numerator and denominator.

2. Change the decimal 0.0205 to a fraction.

   

   Create a “fraction” with 0.0205 in the numerator and 1.0 in the denominator:

   

   Move the decimal point in the 0.0205 four places to the right to turn the numerator into a whole number; move the decimal point in the denominator the same number of places:

   

   Drop the decimal points, plus any leading or trailing zeros in both the numerator and denominator.

   

   Both the numerator and denominator are divisible by 5, so reduce this fraction:

   

Practice questions

1. Change the decimal 0.27 to a fraction.

2. Convert the decimal 0.0315 to a fraction.

3. Write 45.12 as a mixed number.

4. Change 100.001 to a mixed number.

Following are answers to the practice questions:

1. 

   Create a “fraction” with 0.27 in the numerator and 1.0 in the denominator. Then move the decimal points to the right until both the numerator and denominator are whole numbers:

   

   At this point, you can drop the decimal points and trailing zeros.

2. 

   Create a “fraction” with 0.0315 in the numerator and 1.0 in the denominator. Then move the decimal points in both the numerator and denominator to the right one place at a time. Continue until both the numerator and denominator are whole numbers:

   

   Drop the decimal points and trailing zeros. The numerator and denominator are both divisible by 5, so reduce the fraction:

   

3. 

   Before you begin, separate out the whole number portion of the decimal (45). Create a “fraction” with 0.12 in the numerator and 1.0 in the denominator. Move the decimal points in both the numerator and denominator to the right until both are whole numbers:

   

   Drop the decimal points and trailing zeros. As long as the numerator and denominator are both divisible by 2 (that is, even numbers), you can reduce this fraction:

   

   To finish up, reattach the whole number portion that you separated at the beginning.

4. 

   Separate out the whole number portion of the decimal (100) and create a “fraction” with 0.001 in the numerator and 1.0 in the denominator. Move the decimal points in both the numerator and denominator to the right one place at a time until both are whole numbers:

   

   Drop the decimal points and trailing zeros and reattach the whole-number portion of the number you started with: