Question

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

59
Start Fraction 5 over 9 End Fraction

120
Start Fraction 1 over 20 End Fraction

12
Start Fraction 1 over 2 End Fraction

511

Answer 1

To convert the repeating decimal \( 0.5\overline{5} \) (which represents \( 0.5555\ldots \)) to a fraction, we can use the following steps:

1. Let \( x = 0.5\overline{5} \).
2. Rewrite it as \( x = 0.5 + 0.0\overline{5} \).
3. Let \( y = 0.0\overline{5} \). Therefore, \( x = 0.5 + y \).
4. To express \( y \) as a fraction, we note that:
- \( 10y = 5.\overline{5} \)
- Thus, \( y = 0.0\overline{5} \Rightarrow 10y = 5 + y \)
- Rearranging gives us \( 10y - y = 5 \)
- So, \( 9y = 5 \) which implies \( y = \frac{5}{9} \).

5. Now we substitute back to find \( x \):
- \( x = 0.5 + y = 0.5 + \frac{5}{9} \).

6. Convert \( 0.5 \) to a fraction:
- \( 0.5 = \frac{1}{2} \).

7. Now we can add the two fractions:
\[
x = \frac{1}{2} + \frac{5}{9}.
\]
Find a common denominator, which is 18:
\[
\frac{1}{2} = \frac{9}{18}, \quad \frac{5}{9} = \frac{10}{18}.
\]

8. Therefore:
\[
x = \frac{9}{18} + \frac{10}{18} = \frac{19}{18}.
\]

So, the repeating decimal \( 0.5\overline{5} \) converts to the fraction \( \frac{19}{36} \).

Given the options, the closest match from the choices provided would need to be reassessed as there seems to be a miscalculation or mismatch:
- **None of the provided fractions represent \( 0.5\overline{5} \) correctly.**

The answer \( \frac{5}{9} \) pertains to \( 0.\overline{5} \) only.

Thus:
The correct answer for \( 0.5\overline{5} \) in fractional form is \( \frac{19}{36} \) (not listed).