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

Question

., start overline, 6, 4, end overline
.
64

Answer 1

The repeating decimal . overline{64} can be represented as a fraction as follows:

Let x = . overline{64}

Since there is a 2-digit repeating block, we multiply both sides of the equation by 100 to move the decimal point two places to the right:

100x = 64. overline{64}

Subtracting the original equation from the new equation eliminates the repeating part on the right side:

100x - x = 64. overline{64} - . overline{64}
=> 99x = 64
=> x = 64/99

Therefore, the repeating decimal . overline{64} can be written as the fraction 64/99.