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

Question

point, 6 3 overline

Answer 1

To convert the repeating decimal 0.63 overline to a fraction in simplest form, we can let x = 0.63 overline.

We can multiply both sides of the equation by 100 to eliminate the decimal point:

100x = 63.6363 overline

Subtracting the original equation from this new equation, we get:

100x - x = 63.6363 overline - 0.63 overline

99x = 63

Dividing both sides by 99, we find:

x = 63/99

This fraction can be simplified further. Both the numerator and denominator are divisible by 9:

63/99 = (7 * 9)/(11 * 9) = 7/11

Therefore, the repeating decimal 0.63 overline can be written as the fraction 7/11 in simplest form.