The decimal expansion of frac{2517}{6250} wil | vedclass

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(C) To find the number of decimal places after which the decimal expansion of $\frac{2517}{6250}$ terminates,we need to express the denominator in the

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(C) To find the number of decimal places after which the decimal expansion of $\frac{2517}{6250}$ terminates,we need to express the denominator in the form $2^n 	imes 5^m$.First,find the prime factorization of the denominator $6250$:$6250 = 625 	imes 10 = 5^4 	imes (2 	imes 5) = 2^1 	imes 5^5$.The decimal expansion of a rational number $\frac{p}{q}$ terminates after $k$ decimal places,where $k = \max(n, m)$ in the prime factorization $q = 2^n 	imes 5^m$.Here,$n = 1$ and $m = 5$.Therefore,$k = \max(1, 5) = 5$.The decimal expansion will terminate after $5$ decimal places.

The decimal expansion of $\frac{2517}{6250}$ will terminate after how many decimal places?

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