Question

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

1/2

1/20

5/11

5/9

Answer 1

To convert the repeating decimal \(0.5\overline{5}\) (which is 0.5555...) to a fraction, you can use the following method:

1. Let \(x = 0.5\overline{5}\).
2. Then \(x = 0.5555...\).
3. Multiply \(x\) by 10 to shift the decimal point:
\[
10x = 5.5555...
\]
4. Now, subtract the first equation from the second equation:
\[
10x - x = 5.5555... - 0.5555...
\]
This simplifies to:
\[
9x = 5
\]
5. Now, solve for \(x\):
\[
x = \frac{5}{9}
\]

Therefore, the repeating decimal \(0.5\overline{5}\) is equivalent to the fraction \(\frac{5}{9}\).

So, the correct answer is \(5/9\).