Write the repeating decimal as a fration 0.1717...
To express the repeating decimal 0.171717... as a fraction, we use the following steps:
Let's call x the repeating decimal we want to convert:
x = 0.171717...
Since the digits 17 are repeating, we multiply x by 100 to move two decimal places to the right:
100x = 17.171717...
Now, we subtract the original x from this 100x to get rid of the repeating part:
100x - x = 17.171717... - 0.171717...
This yields:
99x = 17
Now we can solve for x by dividing both sides by 99:
x = 17 / 99
The fraction form of the repeating decimal 0.171717... is 17/99.