If the denominator of a fraction has factors other than 2 and 5, the decimal expression.

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Repeats

Is that of a whole number

Has equal numerator and denominator

Terminates

answer is A.

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Detailed Solution

Concept: Here, we’ll use the method of prime factorisation and then divide the fraction, get the decimal and observe its decimal expansion. Let’s assume some examples of (i)120=12×2×5=0.05
Here, the factors of the denominator 2 and 5 are obtained in decimal form that is 0.05. We can see that the decimal terminates in this case.
(ii)16=13×2
There are prime factors in the denominator other than 2 or 5. We have factor 3 also.
Now, Dividing the fraction,
16=0.166666...
From above it's clearly visible that the decimal is non-terminating and is repeating.
(iii)121=13×7
The prime factors of the denominator are 3×7 .
Dividing the fraction, we get 121=0.04761904761......
From above it's clearly visible that the decimal is non-terminating and is repeating.
Hence, If the denominator of a fraction has factors other than 2 and 5 then, the decimal expansion repeats.

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