Question

Convert 0.18¯¯¯¯¯ to a fraction.(1 point) Responses 18101 18 over 101 9500 9 over 500 211 2 over 11 950

Answer 1

To convert the repeating decimal \( 0.18\overline{18} \) (which means the digits "18" repeat indefinitely) into a fraction, we can follow these steps:

Let:
\[ x = 0.181818...\]

Next, we can multiply both sides of the equation by 100 (since the repeating block is two digits long):
\[ 100x = 18.181818...\]

Now, we can subtract the first equation from the second:
\[ 100x - x = 18.181818... - 0.181818...\]
This simplifies to:
\[ 99x = 18\]

Now, solve for \( x \):
\[ x = \frac{18}{99}\]

Next, we simplify the fraction:
\[ \frac{18}{99} = \frac{2}{11} \]
(after dividing both the numerator and the denominator by 9).

Thus, \( 0.18\overline{18} \) as a fraction is:
\[
\boxed{\frac{2}{11}}
\]