The decimal expansion of the rational number | vedclass

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(A) To find the decimal expansion,we express the denominator in the form $2^n \cdot 5^m$.The given number is $\frac{33}{2^2 \cdot 5^1}$.To make the po

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two decimal places

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(A) To find the decimal expansion,we express the denominator in the form $2^n \cdot 5^m$.The given number is $\frac{33}{2^2 \cdot 5^1}$.To make the powers of $2$ and $5$ equal,we multiply the numerator and denominator by $5^{(2-1)} = 5^1$.$\frac{33 \cdot 5}{2^2 \cdot 5^1 \cdot 5^1} = \frac{165}{2^2 \cdot 5^2} = \frac{165}{(2 \cdot 5)^2} = \frac{165}{10^2} = \frac{165}{100} = 1.65$.The decimal expansion terminates after $2$ decimal places.

The decimal expansion of the rational number $\frac{33}{2^{2} \cdot 5}$ will terminate after

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