Question

what fraction is equivalent to (0.overline{5})? type a number in each box. (\frac{quad}{quad}) +

Explanation:

Step1: Let variable equal repeating decimal

Let $x = 0.\overline{5}$, which means $x = 0.5555...$

Step2: Multiply by 10 to shift decimal

$10x = 5.5555...$

Step3: Subtract original equation

Subtract $x$ from $10x$ to eliminate repeating decimals:
$10x - x = 5.5555... - 0.5555...$
$9x = 5$

Step4: Solve for x

$x = \frac{5}{9}$

Answer:

$\frac{5}{9}$