The value of overline{0.037}, where overline{ | vedclass

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Question

(B) Let $x = 0.037037037...$ $(1)$Multiply both sides by $1000$:$1000x = 37.037037037...$ $(2)$Subtract equation $(1)$ from equation $(2)$:$1000x - x

Vedclass · Accepted Answer

$\frac{1}{27}$

Vedclass · Answer

(B) Let $x = 0.037037037...$ $(1)$Multiply both sides by $1000$:$1000x = 37.037037037...$ $(2)$Subtract equation $(1)$ from equation $(2)$:$1000x - x = 37.037037... - 0.037037...$$999x = 37$$x = \frac{37}{999}$Divide both numerator and denominator by $37$:$x = \frac{37 \div 37}{999 \div 37} = \frac{1}{27}$.Since the question asks for the value and $\frac{1}{27}$ is the simplest form, the correct option is $B$.

The value of $\overline{0.037}$, where $\overline{0.037}$ represents the repeating decimal $0.037037037...$, is:

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