Question

equivalent to 0.\overline{1}? each box.

Explanation:

Step1: Recall the definition of a repeating decimal

A repeating decimal \(0.\overline{1}\) (where the bar is over 1) means the digit 1 repeats infinitely, so \(0.\overline{1}=0.1111\cdots\)

Step2: Convert the repeating decimal to a fraction

Let \(x = 0.\overline{1}\), then \(10x=1.\overline{1}\) (multiplying both sides by 10 to move the decimal one place). Subtract \(x\) from \(10x\):
\[

$$\begin{align*} 10x - x&=1.\overline{1}-0.\overline{1}\\ 9x&=1\\ x&=\frac{1}{9} \end{align*}$$

\]

So the fraction equivalent to \(0.\overline{1}\) is \(\frac{1}{9}\) (if the question was about finding the fraction equivalent, assuming the missing part of the question was that).

Answer:

\(\frac{1}{9}\)