Question

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

5/9
Start Fraction 5 over 9 End Fraction

1/20
Start Fraction 1 over 20 End Fraction

1/2
Start Fraction 1 over 2 End Fraction

5/11

Answer 1

To convert \( 0.5\overline{5} \) (or 0.5555...) to a fraction, we can follow these steps:

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

2. To eliminate the repeating decimal, multiply both sides by 10 (since the repeating part is one digit):
\[
10x = 5.5555...
\]

3. Now, subtract the original equation \( x = 0.5555... \) from this new equation:
\[
10x - x = 5.5555... - 0.5555...
\]
which simplifies to:
\[
9x = 5
\]

4. Now, solve for \( x \):
\[
x = \frac{5}{9}
\]

Thus, \( 0.5\overline{5} \) as a fraction is \( \frac{5}{9} \).

The correct answer is:
**5/9**