Question

Convert 0.18¯¯¯¯¯(18 repeating)
to a fraction.(1 point)
Responses

18101
18 over 101

950
9 over 50

211
2 over 11

950

Answer 1

To convert the repeating decimal \(0.18\overline{18}\) to a fraction, we can set \(x = 0.181818...\).

1. First, multiply \(x\) by 100 (since the repeating part has 2 digits):
\[
100x = 18.181818...
\]

2. Now we have two equations:
\[
x = 0.181818...
\]
\[
100x = 18.181818...
\]

3. Subtract the first equation from the second:
\[
100x - x = 18.181818... - 0.181818...
\]
\[
99x = 18
\]

4. Solve for \(x\):
\[
x = \frac{18}{99}
\]

5. Now, simplify the fraction \(\frac{18}{99}\):
The greatest common divisor (GCD) of 18 and 99 is 9, so we divide both the numerator and the denominator by 9:
\[
x = \frac{18 \div 9}{99 \div 9} = \frac{2}{11}
\]

Thus, the repeating decimal \(0.18\overline{18}\) can be expressed as the fraction \(\frac{2}{11}\).

Therefore, the correct response is:
**2 over 11.**