Converting Decimals to Fractions: Part B

In Part A of this lesson, we saw how to convert a terminating decimal number to a fraction. If a decimal is repeating (in other words, after a while, some pattern of digits repeats over and over), then we have to use a different strategy.

Let N be the number, and let n be the number of digits in the repeating block. For example,

0.01 83 ¯

has 2 digits in the repeating block, whereas

0.01 83 ¯

has only 1 .

Setting N equal to its value, multiply both sides of the equation by 10 n . Then subtract N from both sides. You will end up with an equation which you can solve for N as a fractional value.

Example:

Convert the decimal

0.01 83 ¯

into a fraction.

Start with the equation:

N=0.01 83 ¯

There are two digits in the repeating block, so multiply both sides by 10 2 =100 .

100N=1. 83 ¯

Now subtract N from both sides. Notice that the repeating part cancels out.

100N=1. 83 ¯ N=0.01 83 ¯ _ 99N=1.82

Divide both sides by 99 , multiply numerator and denominator by a power of 10 to get rid of the decimal point, and simplify.

N= 1.82 99 = 182 9900 = 91 4950