In the decimal representation of frac{7}{80}, | vedclass

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(D) To find the number of decimal places in the decimal representation of a rational number $\frac{p}{q}$ (where $q 
eq 0$),we first simplify the fra

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(D) To find the number of decimal places in the decimal representation of a rational number $\frac{p}{q}$ (where $q 
eq 0$),we first simplify the fraction to its lowest terms.$\frac{7}{80}$ is already in its simplest form.Next,we find the prime factorization of the denominator $q = 80$.$80 = 2^4 	imes 5^1$.The number of decimal places is given by the maximum exponent of $2$ or $5$ in the prime factorization of the denominator.Here,the exponents are $4$ and $1$. The maximum exponent is $4$.Therefore,the decimal representation of $\frac{7}{80}$ will have $4$ digits after the decimal point.Verification: $\frac{7}{80} = \frac{7 	imes 125}{80 	imes 125} = \frac{875}{10000} = 0.0875$.

In the decimal representation of $\frac{7}{80}$,how many digits will be there after the decimal point?

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