The decimal expansion of frac{43}{2^{4} times | vedclass

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

Question

(B) To find the number of decimal places after which the expansion of a rational number $\frac{p}{q}$ terminates,we express the denominator in the for

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) To find the number of decimal places after which the expansion of a rational number $\frac{p}{q}$ terminates,we express the denominator in the form $2^n 	imes 5^m$.Given the expression: $\frac{43}{2^{4} 	imes 5^{3}}$.To make the powers of $2$ and $5$ equal,we multiply the numerator and denominator by $5^1$:$\frac{43 	imes 5^1}{2^{4} 	imes 5^{3} 	imes 5^1} = \frac{43 	imes 5}{2^{4} 	imes 5^{4}} = \frac{215}{(2 	imes 5)^{4}} = \frac{215}{10^4} = \frac{215}{10000} = 0.0215$.The decimal expansion terminates after $4$ digits.

The decimal expansion of $\frac{43}{2^{4} \times 5^{3}}$ will terminate after .......... digits.

Similar Questions

If $n$ is an odd integer,then $n^{2}-1$ is divisible by...........

Express $404$ as a product of primes.

Determine whether the rational number $\frac{77}{210}$ has a terminating or non-terminating repeating decimal expansion. If it is terminating,write down its decimal expansion.

Show that the square of any positive integer cannot be of the form $6m+2$ or $6m+5$ for any integer $m$.

The last digit of $2^{3} \times 5^{125}$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module