Question

find the rational number of the form p/q corresponding to the decimal representation 0.222...
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Answer 1

Let the 0.2222...be x

x=0.222....

multiply 10 by both the sides

x × 10=0.222...×10

10x=2.222.....

subtract the two equations formed above

10x-x=2.222...-0.222....

9x=2

x=2/9

Answer 2

Step-by-step explanation:

let,

☑ x = 0.222 ..........(1)

recouring digit is 2

multiply by 10 to the both side,

⟹10x = 0.222 x 10

⟹10x = 2.222 ......(2)

☑ subtrack eqn (1) from (2) by right hand and left hand side, we get

⟹10x - x = 2.222 - 0.222

⟹ 9x = 2

x = 2/9

☑ Therefor the p/q form of the given recurring number is

$\boxed{\textbf{\large{2/9}}}$