This shows how to write a repeating decimal as a rational number using geometric series. The first step is to group the irrational number into 3 pairs. You need to separate the number into a group of 2, a group of 4, and a group of 6. . This is shown with the brackets in the picture below. Once you do this you write your pairs in a sequence. You need to make sure to replace the first two numbers of the group of 4 with 2 zeros. You also need to replace the first four numbers of the group of 6 with 4 zeros.
Once you have done this, you determine the first term and the ratio. You find the ratio by dividing any term by the term before it. Once you find your first term and ratio, you can plug them into the infinite geometric sum formula. This is the a(1)/ 1-r. Once you do this you solve. You need to remember when you divide a fraction by a fraction, you get the reciprocal of the second fraction and multiply. Once you do this, the 100's should cancel and you are left with a fraction. You need to make sure to simplify your answer if possible.
