Write 0.083 as a fraction. A) 1/12 B) 1/3 C) 1/6 D) 1/9
The Correct Answer and Explanation is:
Correct choice: A) $\tfrac{1}{12}$
Although the decimal supplied is written as 0.083, in most multiple-choice contexts it is understood to be the rounded form of the repeating decimal 0.083 333 …, whose exact fractional value is $\tfrac{1}{12}$. Here’s why that interpretation makes sense and how to confirm it step by step.
When you see a terminating decimal like 0.083, the safest procedure is to write it over a power of ten:
$$
0.083=\frac{83}{1000}.
$$
If 83 and 1000 shared a common factor, we would divide by it to simplify; however, 83 is prime and does not divide 1000, so $\tfrac{83}{1000}$ is already in lowest terms. That fraction, however, is not among the answer choices. The test designer therefore almost certainly expects you to recognise that the decimal has been rounded to three places rather than written in full.
Look at the four options in decimal form:
- $\tfrac{1}{12}=0.083 333\ldots$ (repeating)
- $\tfrac{1}{3}=0.333 333\ldots$
- $\tfrac{1}{6}=0.166 666\ldots$
- $\tfrac{1}{9}=0.111 111\ldots$
Only $\tfrac{1}{12}$ begins with 0.083. If you round $0.083 333\ldots$ to three decimal places you obtain exactly 0.083. None of the other fractions come close: $0.111$ or $0.167$ or $0.333$ differ too much in the hundredths place.
This pattern—options being simple unit fractions whose decimals repeat—occurs frequently in standardized questions. Writers often list a rounded decimal (three or four digits) and expect you to match it to the fraction whose repeating form produces that decimal when rounded. Recognising those “familiar” repeating decimals (1/3 → 0.333…, 1/6 → 0.166…, 1/9 → 0.111…, 1/12 → 0.0833…) makes answering quick.
Therefore, because only $\tfrac{1}{12}$ yields 0.083 when rounded to three decimal digits, option A is the correct selection.
