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

Question

., start overline, 0, 9, end overline

Answer 1

Let's represent the repeating decimal as x.
To remove the decimal point and the overline, we can multiply x by 100:

100x = 9.999...

Now, we can subtract x from 100x to eliminate the repeating part:

100x - x = 9.999... - 0.999...
99x = 9

Divide both sides of the equation by 99:

x = 9/99

The fraction 9/99 is not in simplest form, as both the numerator and denominator can be divided by 9:

x = 1/11

Therefore, the repeating decimal ., start overline, 0, 9, end overline is equivalent to the fraction 1/11.