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, $\frac{3}{4}$

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:

$9x=5$

$x=\frac{5}{9}$       ............(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:

$900x=175$

$x=\frac{175}{900}$         ............(B)

Now adding equation A and B, we get:

$\frac{5}{9}+\frac{175}{900}$

$\Rightarrow \frac{500}{900}+\frac{175}{900}$

$\Rightarrow \frac{675}{900}$

$\Rightarrow \frac{3}{4}$

Thus, the sum of the given expression is, $\frac{3}{4}$