Without doing any actual division, find which of the following rational number are terminating decimal representation:(1) 716716 (2) 23125(3) 914(4) 3245 (5) 4350(6) 1740(7) 6175(8) 123 250

# Without doing any actual division, find which of the following rational number are terminating decimal representation:(1) $\frac{7}{16}$716 (2) $\frac{23}{125}$(3) $\frac{9}{14}$(4) (5) $\frac{43}{50}$(6) $\frac{17}{40}$(7)(8)

1. A
(1), (3), (5), (6) and (7)
2. B
(1), (2), (5), (6) and (8)
3. C
(1), (3), (5), (6) and (8)
4. D
(1), (2), (5), (6) and (7)

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### Solution:

Concept-  In mathematics, rational numbers are expressed in pq format. Where q is non-zero. It is one of the most important math subjects. Fractions with a non-zero denominator are rational numbers.
Condition for terminating decimal is- If the prime factors in the denominator of the  lowest form of the fraction contain only 2 and / or 5 or no prime factors at all, then the fraction is an end decimal.
Let us check the condition for the given fractions
1) , Terminating decimal
2) Terminating decimal
3) Non Terminating
4) Not-Terminating
5) Terminating decimal
6) Not-Terminating
7) Not-Terminating
8) Terminating decimal
Hence, the correct answer is option 2) (1), (2), (5), (6) and (8)

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