Question

Convert 0.18¯¯¯¯¯ to a fraction.(1 point)
Responses

211
2 over 11

18101
18 over 101

950
9 over 50

9500

Answer 1

To convert the repeating decimal \( 0.18\overline{18} \) to a fraction, we can follow these steps:

Let \( x = 0.181818...\).

Now, multiply \( x \) by 100 (to move the decimal point two places to the right, where the repeating part starts):

\[
100x = 18.181818...
\]

Now, subtract the original equation from this new equation to eliminate the repeating decimal:

\[
100x - x = 18.181818... - 0.181818...
\]
\[
99x = 18
\]

Now, solve for \( x \):

\[
x = \frac{18}{99}
\]

Next, simplify the fraction. The greatest common divisor (GCD) of 18 and 99 is 9:

\[
x = \frac{18 \div 9}{99 \div 9} = \frac{2}{11}
\]

Therefore, the fraction equivalent of \( 0.18\overline{18} \) is:

\(\frac{2}{11}\)

Thus, the correct response is:

**2 over 11**