# Converting between Fractions and Decimals

- - Pre-Algebra

Fractions and decimals are widely used in business and everyday life. They represent parts of a whole just as percent does. A fraction is one or more of the equal parts into which a whole is divided while a decimal is a tenth part, which refers to a decimal numeral system which has ten as its base.

To change a fraction to a decimal, we simply divide the numerator by the denominator. The result would be a terminating decimal, repeating decimal, or non-terminating decimal.

Examples:
1. $\displaystyle \frac{2}{5}=0.4$ since 2 divided by 5 is 0.4

2. $\displaystyle\frac{1}{3}=0.\bar{3}$ since 1 divided by 3 is 0.333...

To change a terminating decimal, rewrite the decimals as decimal fractions and reduce to lowest terms. (A decimal fraction is a fraction whose denominator can be expressed as a power of 10.)

Examples:
1. $0.5=\displaystyle \frac{5}{10}=\displaystyle \frac{1}{2}$

2. $1.05=1\displaystyle \frac{5}{100}=1\displaystyle \frac{1}{20}$

To change a repeating decimal to a fraction, represent each repeating digit by 9 and each non-repeating digit by 0 in the denominator. The numerator is the difference between the number formed by the decimal digits and the number formed by the digits that do not repeat.

Examples:
1. $0.2\bar{5}=\displaystyle \frac{25-2}{90}=\displaystyle \frac{23}{90}$

2. $1.15\overline{325}=1+\displaystyle \frac{15325-15}{99900}=1+\displaystyle \frac{15310}{99900}=1+\displaystyle \frac{1531}{9990}=1\displaystyle \frac{1531}{9990}$