How to Simplify Fractions With Decimals

By Bryan Keythman; Updated April 24, 2017
You can convert the right side of a decimal into a fraction.

Fractions and decimals are parts of whole numbers written in two different forms. A fraction has a numerator over a denominator, which represents the number of parts you have of a whole number over the number of parts by which the whole number is divided. A decimal contains part of a whole number to the right of a decimal point. If a fraction contains a decimal in either its numerator or denominator, you can convert the decimal into a fraction so that you have two similar number formats to simplify the fraction. A fraction is simplified when the only common factor of the numerator and denominator is 1.

Determine a fraction with a decimal that you want to simplify. For the following example, use the fraction 0.2/2.

Convert the decimal to a fraction by placing the number to the right of the decimal point as a numerator over a denominator that corresponds to the place value of the decimal number. In the example, the decimal 0.2 extends to the tenths place, so place 2 as a numerator over 10 as a denominator, which equals 2/10. This leaves (2/10)/2, which consists of a fraction within a fraction.

Divide the numerator by the denominator, which is equivalent to multiplying the numerator by the reciprocal of the denominator, to convert the fraction within a fraction to a single fraction. A reciprocal is a fraction flipped upside down. In the example, divide 2/10 by 2, which is equivalent to multiplying 2/10 by 1/2. This equals 2/20.

Find the largest number that divides evenly into the numerator and denominator of the fraction. In the example, 2 is the largest number that divides evenly into 2 and 20.

Divide both the numerator and denominator by the largest number that divides evenly into both to simplify the fraction. In the example, divide 2 by 2, which equals 1, and divide 20 by 2, which equals 10. This leaves 1/10, which is the simplified form of the fraction with a decimal.