Converting a Fraction Into a Repeating Decimal Number

Fractions can be written as decimal numbers using long division. However, when the denominator of a fraction has a factor other than 2 or 5, the quotient will be a repeating decimal number. Consider the following fraction. 7/15 It is possible to write this fraction as a decimal in two steps.

1

Use Long Division

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Divide the numerator by the denominator using long division.

After some point, the remainder does not become zero and a particular digit or set of digits in the quotient keeps repeating. This means that the quotient is a repeating decimal number.