Question

which fraction represents the decimal (0.overline{12})?
(\bigcirc) (\frac{1}{12})
(\bigcirc) (\frac{3}{25})
(\bigcirc) (\frac{4}{33})
(\bigcirc) (\frac{33}{4})

Explanation:

Step1: Recall the formula for repeating decimals

A repeating decimal with two repeating digits \(0.\overline{ab}\) can be written as \(\frac{ab}{99}\), where \(ab\) is the two - digit repeating part. Here, the decimal is \(0.\overline{12}\), so using the formula, it can be written as \(\frac{12}{99}\).

Step2: Simplify the fraction

Simplify \(\frac{12}{99}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. \(\frac{12\div3}{99\div3}=\frac{4}{33}\).
We can also check the other options:

• For \(\frac{1}{12}\approx0.0833\), which is not equal to \(0.\overline{12}\).
• For \(\frac{3}{25} = 0.12\) (a terminating decimal), not a repeating decimal.
• For \(\frac{33}{4}=8.25\), which is not equal to \(0.\overline{12}\).

Answer:

C. \(\frac{4}{33}\) (assuming the options are labeled A: \(\frac{1}{12}\), B: \(\frac{3}{25}\), C: \(\frac{4}{33}\), D: \(\frac{33}{4}\))