Question

1. what fraction is equivalent to 0.033̅?

3/100
3/10
1/30
1/3

Explanation:

Step1: Let \(x = 0.0\overline{33}\).

Then \(10x=0.\overline{33}\) and \(1000x = 33.\overline{33}\).

Step2: Subtract \(10x\) from \(1000x\).

\(1000x-10x=33.\overline{33}- 0.\overline{33}\).
Since \(33.\overline{33}-0.\overline{33}=33\), and \(1000x - 10x=990x\), we have \(990x = 33\).

Step3: Solve for \(x\).

\(x=\frac{33}{990}=\frac{1}{30}\)

Answer:

C. \(\frac{1}{30}\)