Question

Write the recurring decimal 0.2 as a fraction in its simplest form.

Answer 1

`0.\.{2}=(2)/(9)`

Step-by-step explanation:

Let x equal the recurring decimal:

`x=0.\.{2}=0.2222\dots`

Multiply both sides by 10:

`\implies 10x=2.222\dots`

Eliminate the recurring part of the decimal by subtracting the equation of x from the equation of 10x:

`\begin{array}{ l r c l}& 10x & = & 2.222...\\\\- & x & = & 0.2222...\\\\\cline{1-4}\\& 9x & = & 2\end{array}`

Divide both sides by 9:

`\implies x=(2)/(9)`

Answer 2

`\sf \bold{(2)/(9)} }`

Step-by-step explanation:

Recurring decimal means the number keeps repeating.

0.2 is the recurring digit

x = 0.2222...

10x = 2.2222...

10x -x = 2

9x = 2

x = 2/9

0.222... ≈ 2/9