Convert the following repeating decimal to a fraction in sir .5overline (3) Answer Attempt 1 out of 3 square

## Step 1: Set up the equation<br />### Let $x$ equal the repeating decimal $0.5\overline{3}$. So, $x = 0.5333...$<br />## Step 2: Multiply by 10<br />### Multiply both sides of the equation by 10 to move the non-repeating part to the left of the decimal: $10x = 5.3333...$<br />## Step 3: Multiply by 10 again<br />### Multiply both sides of the original equation by 100 to shift the repeating part one cycle to the left of the decimal: $100x = 53.3333...$<br />## Step 4: Subtract the equations<br />### Subtract the equation from Step 2 from the equation in Step 3: $100x - 10x = 53.3333... - 5.3333...$, which simplifies to $90x = 48$.<br />## Step 5: Solve for x<br />### Divide both sides by 90: $x = \frac{48}{90}$.<br />## Step 6: Simplify the fraction<br />### Simplify the fraction by dividing both numerator and denominator by their greatest common divisor (6): $x = \frac{48 \div 6}{90 \div 6} = \frac{8}{15}$.