Repeating Decimals

Repeating decimals are decimals that go on forever and ever such as .33333333 or .6666666666667. These decimals are also fractions such as 1/3 and 2/3 and there is a way to convert them. The first thing you do is write the decimals as a geometric sequence. For example 0.3 +0.03+0.003+0.0003 etc. Once you do this you can find the rate which is 10 and use that for r. After that you use the equation a1/1-r and you plug in the corresponding numbers. For a1 you would plug in the first number of the sequence which is 0.3 and for r you would use the rate you found so 1/10. Once you simplify this equation you get 1/3. Here is an example of repeating decimals.