Question

the value of 4.6bar + 0.2bar is​

Answer 1

As 0.46666......+0.2222222=4.888888888

Answer 2

The value is $4.\bar{6}+0.\bar{2}=\frac{44}{9}$

Step-by-step explanation:

To find : The value of 4.6bar + 0.2bar ?

Solution :

Let $x=4.666...$  ....(1)

Multiply 10 both side,

$10x=46.666...$  ....(2)

Subtract (1) from (2),

$10x-x=(46.666...)-(4.666...)$

$9x=42$

$x=\frac{42}{9}$

So, $4.\bar{6}=\frac{42}{9}$

Let $y=0.222...$  ....(3)

Multiply 10 both side,

$10y=2.222...$  ....(4)

Subtract (3) from (4),

$10y-y=(2.222...)-(0.222...)$

$9y=2$

$y=\frac{2}{9}$

So,  $0.\bar{2}=\frac{2}{9}$

Substitute,

$4.\bar{6}+0.\bar{2}=\frac{42}{9}+\frac{2}{9}$

$4.\bar{6}+0.\bar{2}=\frac{42+2}{9}$

$4.\bar{6}+0.\bar{2}=\frac{44}{9}$

Therefore, the value is $4.\bar{6}+0.\bar{2}=\frac{44}{9}$

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