Question

`Problem: Compute the sum 0.\overline{5} + 0.19\overline{4}.`

Answer 1

Ii think it's 0.7499996
I'm not sure

Answer 2

Answer : The sum of the given expression is,
`(3)/(4)`

Step-by-step explanation :

As we are given the expression:

`0.\bar{5}+0.19\bar{4}`

Let us assumed that,

`x=0.\bar{5}`

or,

`x=0.5555.......` ..........(1)

To shifting the one decimal place to the right, we are multiplying the equation by 10 on both side, we get:

`10x=5.5555.......` ...........(2)

Now subtracting equation 1 from 2, we get:

`9x=5`

`x=(5)/(9)` ............(A)

and,

Let us assumed that,

`x=0.19\bar{4}`

or,

`x=0.194444.......` ..........(1)

To shifting the two decimal place to the right, we are multiplying the equation by 100 on both side, we get:

`100x=19.4444.......` ...........(2)

To shifting the one more decimal place to the right, we are multiplying the equation by 10 on both side, we get:

`1000x=194.4444.......` ...........(3)

Now subtracting equation 2 from 3, we get:

`900x=175`

`x=(175)/(900)` ............(B)

Now adding equation A and B, we get:

`(5)/(9)+(175)/(900)`

`\Rightarrow (500)/(900)+(175)/(900)`

`\Rightarrow (675)/(900)`

`\Rightarrow (3)/(4)`

Thus, the sum of the given expression is,
`(3)/(4)`