Convert the following repeating decimal to a fraction in simplest form.
., start overline, 2, 8, end overline
.
28
The repeating decimal ., start overline, 2, 8, end overline can be represented as x.
To convert it to a fraction, we'll start by multiplying x by a power of 10 to eliminate the decimal and repeating part:
10x = 28., start overline, 2, 8, end overline
Next, we subtract x from 10x to eliminate the repeating part:
10x - x = 28., start overline, 2, 8, end overline - ., start overline, 2, 8, end overline
9x = 28
Now, we solve for x:
x = 28 / 9
Therefore, the fraction in simplest form is 28/9.