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Question

(B) The given number $0.123123123...$ can be written as $0.\overline{123}$.Since the decimal expansion is non-terminating and repeating,it can be expr

Vedclass · Accepted Answer

a rational number

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(B) The given number $0.123123123...$ can be written as $0.\overline{123}$.Since the decimal expansion is non-terminating and repeating,it can be expressed in the form $\frac{p}{q}$,where $p$ and $q$ are integers and $q 
eq 0$.Let $x = 0.123123...$ (Equation $1$).Multiplying both sides by $1000$,we get $1000x = 123.123123...$ (Equation $2$).Subtracting Equation $1$ from Equation $2$:$1000x - x = 123.123123... - 0.123123...$$999x = 123$$x = \frac{123}{999} = \frac{41}{333}$.Since the number can be expressed as a ratio of two integers,it is a rational number.

$0.123123123...$ is

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