Convert the following repeating decimal to a fraction in simplest form.
., start overline, 5, end overline
Let x = 0.5555...
Multiplying both sides of the equation by 1000, we have:
1000x = 555.5555...
Subtracting the original equation from this new equation, we have:
1000x - x = 555.5555... - 0.5555...
Simplifying both sides, we get:
999x = 555
Dividing both sides by 999, we have:
x = 555/999
Simplifying the fraction, we get:
x = 5/9
Therefore, the repeating decimal 0.5555... is equal to 5/9 in simplest form.