Convert the following repeating decimal to a fraction in simplest form.
., start overline, 1, 7, end overline
.
17
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)
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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.