Question

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

59
Start Fraction 5 over 9 End Fraction

12
Start Fraction 1 over 2 End Fraction

511
Start Fraction 5 over 11 End Fraction

120
Start Fraction 1 over 20 End Fraction

Answer 1

To convert \(0.5\overline{0}\) (which means 0.50000...) to a fraction, we'll follow these steps:

1. Let \(x = 0.5\overline{0}\).

2. To eliminate the repeating decimal, we multiply both sides of the equation by 10:

\[
10x = 5.0\overline{0}
\]

3. Now we can subtract the original \(x\) from this new equation:

\[
10x - x = 5.0\overline{0} - 0.5\overline{0}
\]

This simplifies to:

\[
9x = 4.5
\]

4. Now, divide both sides by 9 to solve for \(x\):

\[
x = \frac{4.5}{9}
\]

5. We can convert \(4.5\) to a fraction:

\[
4.5 = \frac{45}{10} = \frac{9}{2}
\]

So we have:

\[
x = \frac{9/2}{9} = \frac{9}{2 \times 9} = \frac{9}{18} = \frac{1}{2}
\]

Thus, the fraction representing \(0.5\overline{0}\) is:

\[
\frac{1}{2}
\]

The correct response is:

\[
\text{Start Fraction 1 over 2 End Fraction}
\]