Converting repeating decimal to fraction

The “period” of a repeating decimal begins immediately after the decimal point. Sometimes, this is referred to as the repeated block.

Write the period of the repeating decimal in the numerator of an ordinary fraction and write some number of nines in the denominator of an ordinary fraction. The number of nines must be equal to the number of digits in the period of the repeating decimal.

Take a repeating decimal 0.3 as an example. (A bar over the three is usually used to indicate the three is repeating). It has zero integers and a three in the period, the place after the decimal point.

Convert to a fraction.

The rule states that the period of a repeating decimal should be written in the numerator of an ordinary fraction. So, in the numerator we write 3.

The denominator must contain some number of nines. In this case, the number of nines must be equal to the number of digits in the period of the repeating decimal 0.3.

In the repeating decimal the period consists of one three. So, we write one nine in the denominator of the fraction: 3/9
 
The resulting fraction 3/9 can be reduced by 3, and then we get the following: 1/3
 
Thus, when one translates the repeating decimal 0.3 into an ordinary fraction, one gets 1/3.

Want to try 0.45 repeating? The answer will be 5/11.