Question

Express 0.2222 as a rational number

Answer 1

Answer :

0.222... = 2/9

Solution :

Let X = 0.222... -------(1)

Now ,

Multiplying eq-(1) by 10 , we have ;

=> 10 × X = 10 × 0.222...

=> 10X = 2.222... -----(2)

Now ,

Subtracting eq-(1) from the eq-(2) , we have ;

=> 10X - X = 2.222... - 0.222...

=> 9X = 2

=> X = 2/9

=> 0.222... = 2/9

Hence 0.222... = 2/9

Answer 2

Question:

$\sf Express \: 0.\overline{2} \: as \: a \: rational \: number$

Answer:

$\sf \: \dfrac{2}{9} \: is \: the \: rational \: form$

Solution:

$\sf Let \: x = 0.\overline{2} \: \: \: \: ...(1)$

$\sf 10x = 2.\overline{2} \: \: \: \: ...(2)$

Subtract ( 1 ) from (2)

[ If equals are subtracted from equal, the wholes are equal ]

⟹ $\sf 2.\overline{2}-0.\overline{2}= 10x-x$

⟹ $\sf \: 2 = 9x$

⟹ $\sf \: \dfrac{2}{9} = x$

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( We could verify our answer by dividing 2 by 9

2/9 = 0.222..... ]