Question

Without actually performing the long division, the terminating decimal expansion of 51/1500 is in the form of 17/2^nx5^m, then (m+n) is equal to

Answer 1

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Answer 2

Solution :-

→ 51/1500

→ (17 * 3)/(500 * 3)

→ (17/500)

now, checking prime factors of denominator we get,

→ 500 = 2 * 2 * 5 * 5 * 5 = 2² * 5³

then,

→ (17/500)

→ 17/(2² * 5³) = 17/2^n * 5^m

comparing both denominator we get,

→ 2² * 5³ = 2^n * 5^m

therefore,

→ n = 2

→ m = 3

hence,

→ (m + n) = 2 + 3 = 5 (Ans.)

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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