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

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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.

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