The decimal expansion of frac{18}{5^{3}} will | vedclass

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(C) To find the number of decimal places for a rational number $\frac{p}{q}$ where $q = 2^n \cdot 5^m$,the number of decimal places is given by $\max(

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) To find the number of decimal places for a rational number $\frac{p}{q}$ where $q = 2^n \cdot 5^m$,the number of decimal places is given by $\max(n, m)$.Given the expression $\frac{18}{5^3}$,we can rewrite the denominator as $2^0 \cdot 5^3$.Here,$n = 0$ and $m = 3$.The number of decimal places is $\max(0, 3) = 3$.Alternatively,$\frac{18}{5^3} = \frac{18 \cdot 2^3}{5^3 \cdot 2^3} = \frac{18 \cdot 8}{10^3} = \frac{144}{1000} = 0.144$.Since there are $3$ digits after the decimal point,the correct option is $C$.

The decimal expansion of $\frac{18}{5^{3}}$ will terminate after how many decimal places?

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