Convert the following repeating decimal to a fraction in simplest form.

Question

., start overline, 1, 7, end overline
.
17

Answer 1

The repeating decimal ., start overline, 1, 7, end overline is represented as follows:

.171717...

To convert this repeating decimal to a fraction, we can use the fact that x = .171717... is equal to 100x = 17.171717...:

100x = 17.171717...
- x = 0.171717...

99x = 17 (subtract the above equations)
------------
99x = 17

Now we can divide both sides by 99 to solve for x:

x = 17/99

Therefore, the repeating decimal ., start overline, 1, 7, end overline is equivalent to the fraction 17/99.