Question

if 241/4000=241/2m*5n,find the value of mand n.hence write its decimal expansion without actual division

Answer 1

Solution :

4000 = 2×2×2×2×2×5×5×5

= $2^{5}\cdot5^{3}$

Now ,

$\frac{241}{4000}=\frac{241}{2^{m}\cdot5^{n}}$

$\implies\frac{241}{2^{5}\cdot5^{3}}=\frac{241}{2^{m}\cdot5^{n}}$

$\rm\textsf{Compare \:both\: sides, \:we\:get }$

=> m = 5 ,n = 3

And

241/4000

= $\frac{241}{2^{5}\cdot5^{3}}$

= $\frac{241\cdot5^{2}}{2^{5}\cdot5^{5}}$

= $\frac{6025}{\left(2\cdot5\right)}$

= $\frac{6025}{\left(10\right)^{5}}$

= $0.06025$

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