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,

has 2 digits in the repeating block, whereas

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

into a fraction.

Start with the equation:

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

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

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