Question

Convert 0.5¯¯¯ to a fraction.(1 point) The fraction equivalent of 0.5¯¯¯ is blank

Answer 1

Let \( x = 0.5\overline{5} \), which means \( x = 0.55555...\)

To convert this repeating decimal to a fraction, we can use the following steps:

1. **Multiply by 10**:
\[
10x = 5.55555...
\]

2. **Set up the equation**:
Now, we have:
\[
x = 0.55555... \quad (1)
\]
\[
10x = 5.55555... \quad (2)
\]

3. **Subtract equation (1) from equation (2)**:
\[
10x - x = 5.55555... - 0.55555...
\]
\[
9x = 5
\]

4. **Solve for \( x \)**:
\[
x = \frac{5}{9}
\]

Thus, the fraction equivalent of \( 0.5\overline{5} \) is \(\frac{5}{9}\).