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

Question

asked Jan 27, 2018 101k views

2 Answers

Jacob Oscarson · Answer 1 · 2018-02-01T00:02:04+0000

Answer : The sum of the given expression is,

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,