If the decimal 0.d25d25d25ldots is expressibl | vedclass

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

Question

(D) Let $x = 0.d25d25d25\ldots$ $(i)$Multiplying by $1000$,we get $1000x = d25.d25d25\ldots$ (ii)Subtracting $(i)$ from (ii),we get $999x = d25$,where

Vedclass · Accepted Answer

$34$

Vedclass · Answer

(D) Let $x = 0.d25d25d25\ldots$ $(i)$Multiplying by $1000$,we get $1000x = d25.d25d25\ldots$ (ii)Subtracting $(i)$ from (ii),we get $999x = d25$,where $d25$ represents the number $100d + 25$.So,$x = \frac{100d + 25}{999}$.Given $x = \frac{n}{27}$,we have $\frac{n}{27} = \frac{100d + 25}{999}$.Multiplying both sides by $27$,we get $n = \frac{100d + 25}{37}$.For $n$ to be an integer,$100d + 25$ must be divisible by $37$.Testing values for $d \in \{1, 2, \ldots, 9\}$:If $d = 9$,$100(9) + 25 = 925$.$925 / 37 = 25$,which is an integer.Thus,$d = 9$ and $n = 25$.Therefore,$d + n = 9 + 25 = 34$.

If the decimal $0.d25d25d25\ldots$ is expressible in the form $n/27$,then $d+n$ must be

Similar Questions

$A$ student has to answer $10$ out of $13$ questions in an examination,choosing at least $5$ questions from the first $6$ questions. The number of choices available to the student is:

The locus of the point $z = x + iy$ satisfying the equation $\left|\frac{z-1}{z+1}\right| = 1$ is given by:

Smoke is an example of ...

In the process of transcription,the sigma factor is important for:

$A$ body cools from $62^{\circ}C$ to $50^{\circ}C$ in $10$ minutes and to $42^{\circ}C$ in the next $10$ minutes. The temperature of the surrounding is ........... $^{\circ}C$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module