Question

Which of the following is a rational number having terminating decimal expansion: (a) 36/7 (b) 41/80 (c) 329/409 (d) All of these options​

Answer 1

Answer:

option "b" that is 41/80

Answer 2

Solution :-

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 prime factors of denominators of given fractions we get,

a) 36/7

→ 7 = 1 * 7

since prime factors of denominator are other than 2 and 5 , the given fraction is a non terminating decimal expansion .

b) 41/80

→ 80 = 2 * 2 * 2 * 2 * 5

since prime factors of denominator are 2 and 5 only , the given fraction is a terminating decimal expansion .

c) 329/409

→ 409 = 1 * 409

since prime factors of denominator are other than 2 and 5 , the given fraction is a non terminating decimal expansion .

Hence, Option (b) is correct answer .

Learn more :-

let a and b positive integers such that 90 less than a+b less than 99 and 0.9 less than a/b less than 0.91. Find ab/46

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