Convert the following repeating decimal to a fraction in simplest form.
., start overline, 1, 0, end overline
Let x = .101010...
Multiplying both sides of the equation by 100, we get:
100x = 10.101010...
Subtracting the equation x = .101010... from 100x = 10.101010..., we get:
99x = 10
Dividing both sides of the equation by 99, we get:
(99x)/99 = 10/99
Simplifying, we have:
x = 10/99
Therefore, the fraction equivalent to .101010... is 10/99 in simplest form.