Question

Convert 0.5--------- to a fraction.

Answer 1

To convert the repeating decimal \( 0.5\overline{0} \) (where the "0" repeats indefinitely) to a fraction, you can follow these steps:

1. Let \( x = 0.5\overline{0} \).
2. This means \( x = 0.500000...\).
3. To eliminate the repeating part, multiply \( x \) by 10 (since the repeating part is one digit long):

\[
10x = 5.000000...
\]

4. Now, set up the equation with the value of \( x \):

\[
10x = 5 + x
\]

5. Subtract \( x \) from both sides to isolate \( x \):

\[
10x - x = 5
\]

\[
9x = 5
\]

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

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

Thus, the repeating decimal \( 0.5\overline{0} \) can be expressed as the fraction \( \frac{5}{9} \).