Question

what fraction is equivalent to (0.overline{1})?
type a number in each box.
(\frac{square}{square})

Explanation:

Step1: Let x equal the repeating decimal

Let $x = 0.\overline{1}$, which means $x = 0.1111...$

Step2: Multiply x by 10 to shift decimal

Since one digit repeats, multiply by 10:
$10x = 1.1111...$

Step3: Subtract original x from 10x

Subtract to eliminate repeating decimals:
$10x - x = 1.1111... - 0.1111...$
$9x = 1$

Step4: Solve for x by dividing both sides

$x = \frac{1}{9}$

Answer:

$\frac{1}{9}$