Convert the following repeating decimal to a fraction in simplest form.
., start overline, 2, 9, end overline
.
29
The given repeating decimal is 0.2929...
To convert this repeating decimal to a fraction, we can use the following method:
Let x = 0.2929...
Multiplying both sides of the equation by 100 (to remove the decimal point), we get:
100x = 29.2929...
Subtracting the original equation from this equation, we get:
100x - x = 29.2929... - 0.2929...
Simplifying both sides of the equation, we get:
99x = 29
Dividing both sides of the equation by 99, we get:
x = 29/99
Therefore, the fraction equivalent to the repeating decimal 0.2929... is 29/99.