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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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?

Similar Questions

The value of $\sqrt{1+1}$ is . . . . . . (Rational,Irrational,Integer).

For the polynomial $p(x) = x^2 - 4x + 3$,the value of $\alpha + \beta$ is . . . . . . .

The Greatest Common Divisor $(GCD)$ of $20 a^{2} b$ and $30 a b^{2}$ is $10 a^{2} b^{2}$. State whether this statement is True or False.

Find the $LCM(26, 91)$.

If the Least Common Multiple $(LCM)$ of $(12, 15, 21) = 500 + 2x$,then $x = $ . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module