Question

6. Which of the following has terminating decimal expansion?
a. 115/14

b.197/200

c.321/15

d.46/2^2×3^2×5​

Answer 1

Step-by-step explanation:

number has a terminating decimal expansion if the digits after the decimal point terminate. The fraction 5/10 has the decimal expansion 0.5

option B is correct

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Answer 2

Solution :-

Concept to be used :- we have to check prime factors of denominators of given fraction .

• if Prime factor are 2, or 5 , or 2 and 5 both . Than the given fraction is a terminating decimal expansion .
• if prime factors are other than 2 or 5 , than the given fraction is a non - terminating decimal expansion .

checking all given options we get,

(a) 115/14

checking prime factors of denominator,

→ 14 = 2 * 7

since prime factors of denominator is 7 which is other than 2 or 5 , therefore, we can conclude that, the given fraction is a non - terminating decimal expansion .

(b) 197/200

checking prime factors of denominator,

→ 200 = 2 * 2 * 2 * 5 * 5

as we can see that, prime factors of denominator are 2 and 5 only, therefore, we can conclude that, the given fraction is a terminating decimal expansion .

(c) 321/15

→ 107/5

as we can see that, prime factors of denominator is 5 only, therefore, we can conclude that, the given fraction is a terminating decimal expansion .

(d) 46/2² * 3² * 5

→ 23/(2 * 3² * 5)

as we can see that, prime factors of denominator is 3 also, which is other than 2 and 5 , therefore, we can conclude that, the given fraction is a non - terminating decimal expansion .

Hence, both (b) and (c) are terminating decimal expansion .

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