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

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Question

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

Vedclass · Accepted Answer

Rational number

Vedclass · Answer

(A) The given number is $0.01111...$,which can be written as $0.0\bar{1}$.
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 $3$).
Subtract 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 of two integers,it is a rational number.

The number $0.01111...$ is a type of........

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