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(B) Let $x = 4.185185185...$ (Equation $1$)Since there are $3$ repeating digits,multiply by $1000$:$1000x = 4185.185185...$ (Equation $2$)Subtract Equ

Vedclass · Accepted Answer

$4 \frac{5}{27}$

Vedclass · Answer

(B) Let $x = 4.185185185...$ (Equation $1$)Since there are $3$ repeating digits,multiply by $1000$:$1000x = 4185.185185...$ (Equation $2$)Subtract Equation $1$ from Equation $2$:$1000x - x = 4185.185185... - 4.185185...$$999x = 4181$$x = \frac{4181}{999}$Now,convert to a mixed fraction:$x = 4 + \frac{181}{999}$Wait,checking the repeating decimal $4.185185...$ as a fraction:$x = 4 + \frac{185}{999}$Simplify $\frac{185}{999}$ by dividing by $37$:$185 \div 37 = 5$$999 \div 37 = 27$So,$x = 4 \frac{5}{27}$.

For each question,select the proper option from four options given,to make the statement true: $4 . \overline{185} = \ldots \ldots$

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