The number 0.01111... is a . . . . . . type | vedclass

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(A) The given number is $0.01111...$,which can be written as $0.0\overline{1}$.Since the decimal expansion is non-terminating and repeating,it can be

Vedclass · Accepted Answer

Rational

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(A) The given number is $0.01111...$,which can be written as $0.0\overline{1}$.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 $x = 0.0111...$ (Equation $1$).Multiply by $10$: $10x = 0.1111...$ (Equation $2$).Multiply by $100$: $100x = 1.1111...$ (Equation $3$).Subtracting Equation $2$ from Equation $3$: $100x - 10x = 1.1111... - 0.1111...$.$90x = 1$.$x = \frac{1}{90}$.Since the number can be expressed as a fraction $\frac{1}{90}$,it is a rational number.

The number $0.01111...$ is a . . . . . . type of number. (Rational,Irrational,Integer)

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