Convert the following repeating decimal to a fraction in simplest form.
., start overline, 3, 6, end overline
Let's represent this repeating decimal as x:
x = 0.363636...
To convert this repeating decimal to a fraction, we can multiply both sides of the equation by a power of 10 to remove the repeating part:
100*x = 36.363636...
Next, we subtract the original equation from the new equation to eliminate the repeating part:
100*x - x = 36.363636... - 0.363636...
99*x = 36
x = 36/99
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 9:
x = (36/9) / (99/9)
x = 4/11
Therefore, the repeating decimal 0.363636... is equivalent to the fraction 4/11 in simplest form.