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

Question

., start overline, 2, 8, end overline
.
28

Answer 1

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.