How many decimal places are there in the deci | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $\frac{3}{113}$?

Similar Questions

If $\alpha$ and $\beta$ are the zeros of the polynomial $P(x) = x^2 - 3x + 2k$ and $\alpha + \beta = \alpha\beta$,then the value of $k$ is:

Explain why $7 \times 11 \times 13 + 13$ and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$ are composite numbers.

What is the Least Common Multiple $(LCM)$ of $36$ and $100$?

The $HCF$ of the smallest prime number and the smallest composite number is . . . . . . .

The largest positive integer that divides $70$ and $125$,leaving remainders $5$ and $8$ respectively,is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module