Question

express 0.1 bar in p by q

Answer 1

Let X = 0.1
x= 0.1 ( first equation )
multiplying both side
10 X = 1.1.... ( second equation )
subtract 2 equation from 1 equation
10 X = 1.1...
X = 0.1...
ans is 9 X = 1
then X = 1/9

Answer 2

$\displaystyle \bf{ 0. \overline{1} = \frac{1}{9} }$

Which is of the form p/q where p , q are integers and q ≠ 0

Given :

The number $\displaystyle \sf{ 0. \overline{1} }$

To find :

To express in the form p/q where p , q are integers and q ≠ 0

Solution :

Step 1 of 2 :

Write down the given number

The given number is $\displaystyle \sf{ 0. \overline{1} }$

Step 2 of 2 :

Express in the form p/q where p , q are integers and q ≠ 0

$\displaystyle \sf{ Let \: \: x = 0. \overline{1} }$

Then x = 0.1111111... - - - - - - - (1)

Multiplying both sides by 10 we get

10x = 1.1111111... - - - - - - (2)

Equation 2 - Equation 1 gives

9x = 1

$\displaystyle \sf{ \implies x = \frac{1}{9} }$

$\displaystyle \sf{ \therefore \: \: 0. \overline{1} = \frac{1}{9}}$

Which is of the form p/q where p , q are integers and q ≠ 0

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