Question

Express 0.6 bar (_) as a rational number is simplest form

Answer 1

Here's your answer

x = 0.666.... (1)
multiplying both side with 10

10x=6.666... (2)

subtracting (1) from (2)
10x-x= 6.666.. - 0.666..
9x= 6
x=6/9 or 2/3

hence,the simplest form of 0.6 bar is 2/3

Answer 2

The simplest form is $\dfrac{2}{3}$.

Step-by-step explanation:

We have,

0.66666....

Let x = 0.666         .... (1)

Express 0.6... as a rational number is simplest form = ?

Multiplying equation (1) by 10 both sides, we get

10x = 6.666             ... (2)

Subtracting (1) from (2) , we get

10x - x = 6.666- 0.666

⇒ 9x = 6

⇒ $x=\dfrac{6}{9}=\dfrac{2}{3}$

Hence, the simplest form is $\dfrac{2}{3}$.