How many decimal places are there in the deci | vedclass

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(D) The number of decimal places in the decimal expansion of a rational number $\frac{p}{q}$ (where $q$ is of the form $2^n \cdot 5^m$) is given by $\

Vedclass · Accepted Answer

$112$

Vedclass · Answer

(D) The number of decimal places in the decimal expansion of a rational number $\frac{p}{q}$ (where $q$ is of the form $2^n \cdot 5^m$) is given by $\max(n, m)$.However,for a fraction $\frac{p}{q}$ where $q$ is not of the form $2^n \cdot 5^m$,the decimal expansion is non-terminating and repeating.For $\frac{3}{113}$,the denominator $113$ is a prime number and is not of the form $2^n \cdot 5^m$.Therefore,the decimal expansion is non-terminating and repeating.If the question implies the length of the period of the repeating decimal,for a prime $p$,the period length divides $p-1$.For $p = 113$,the period length is $112$.

How many decimal places are there in the decimal expansion of $\frac{3}{113}$?

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