Question

if
$\frac{241}{4000} = \frac{241}{ {2}^{n} \times {5}^{m} } find \: the \: value \: of \: n \: and \: m$

Answer 1

Given : $\frac{241}{4000} = \frac{241}{2^n * 5^m}$

$\frac{241}{2 * 2 * 2 * 2 * 2 * 5 * 5 * 5} = \frac{241}{2^n * 5^m}$

$\frac{241}{2^5 * 5^3} = \frac{241}{2^n * 5^m}$


Therefore n = 5, m = 3.


Hope this helps!

Answer 2

Hi☺☺..

$\frac{241}{4000} = \frac{241}{2 {}^{n} \times {5}^{m} } \\ \\ by \: cross \: multiplying \: \\ we \:get \\ \\ {2}^{n} \times {5}^{m} = 4000 \\ \\ {2}^{n} \times {5}^{m} = 4 \times 1000 = {2}^{2} \times {10}^{3} \\ \\ {2}^{n} \times {5}^{m} = {2}^{2} \times {(5 \times 2)}^{3} \\ \\ {2}^{n} \times {5}^{m} = {2}^{2} \times {5}^{3} \times {2}^{3} \\ \\{2}^{n} \times {5}^{m} = {2}^{5} \times {5}^{3} \\ \\ = > n = 5 \: and \: \: m = 3$