1. Convert 0.2 into a fraction.
a. 1/5
b. 11/50
c. 2/9
d. 2/7
2. What is the decimal expansion of 5/6?
a. 0.(56)
b. 0.83
c. 0.56
d. 1.2
Answers and Explanations
1. C: When converting a decimal whose value repeats itself indefinitely, write the repeating digit or digits in the numerator. In this problem, the repeating digit is 2. In the denominator, place 9 for every repeating digit, then reduce the fraction to lowest terms. In this problem a single 9 is in the denominator, so the answer is 2/9. Another example is 0.‾24= 24/99=8/33
2. B: 5/6 can be rewritten as 5÷6=0.83 ?
As you can see, the answer to question 1 is nonsense (real answer is, of course, a). The answer to 2 although mathematically accurate is in the form of a question.
The topic of these two questions would appear to be, "How to convert repeating decimals to fractions and fractions to repeating decimals".
My guess is that the "0.2" in the first question should really have appeared with a horizontal bar above the "2", indicating that the decimal number consists of an infinitely repeating sequence of that particular digit.
Similarly, I would guess that answer "b" to the second question should appear as a "0.83" with a horizontal bar above the "3", indicating that the digit "3" repeats infinitely.
The addition of two bars would make the questions meaningful and the answers correct.
Number 1 is probably a typo... the 2 probably in the 0.2 was meant to have a bar over it as in 0.2222222222.....