Question

Convert 0.5¯¯¯ to a fraction.(1 point)
Responses

120
Start Fraction 1 over 20 End Fraction

12
Start Fraction 1 over 2 End Fraction

511
Start Fraction 5 over 11 End Fraction

59

Answer 1

To convert the repeating decimal \( 0.5\overline{5} \) (which can also be expressed as \( 0.5555\ldots \)) to a fraction, we can use the following method:

Let \( x = 0.5\overline{5} \).

To eliminate the repeating part, we can multiply \( x \) by 10:

\[
10x = 5.5\overline{5}
\]

Now, subtract the original \( x \) from this equation:

\[
10x - x = 5.5\overline{5} - 0.5\overline{5}
\]

This simplifies to:

\[
9x = 5
\]

Now, solve for \( x \):

\[
x = \frac{5}{9}
\]

Therefore, \( 0.5\overline{5} \) is equal to \( \frac{5}{9} \).

Now let's compare this to the answer choices you provided:

- \( 120 \)
- \( \frac{1}{20} \)
- \( \frac{1}{2} \)
- \( \frac{5}{11} \)
- \( 59 \)

None of the answer choices match \( \frac{5}{9} \), so it looks like there might be a misunderstanding or a miscalculation somewhere. The correct answer, based on standard conversion methods, is \( \frac{5}{9} \).