Question

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

Answer 1

Answer:

$0.\.{2}=\dfrac{2}{9}$

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:

$\implies x=\dfrac{2}{9}$

Answer 2

Answer:

$\sf \bold{\dfrac{2}{9}} }$

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