Respuesta :

AprilKitties
So here, I would first multiply 0.17777.... (Assume that that's x) by 10, then you get

10x = 1.777777...

And then subtract x from 10x and then you get 1.6.

So that means that 

10x - x = 9x

and 1.7777... - 0.17777... = 1.6

So now to solve for x, divide both sides by 9

To get 1.6/9 = x

Or 16/90 = x

Or 8/45 = x

(That explanation made no sense)
lublana

Answer:

[tex]\frac{8}{45}[/tex]

Step-by-step explanation:

We are given that

[tex]0.1\bar 7[/tex]

We have to find the value in fraction of given rational number

Let x=[tex]0.1\bar 7[/tex]

Multiply on both side by 10 then we get

[tex]10 x=1.77...[/tex]

[tex]10x=1.6+0.1\bar 7[/tex]

Substitute the value then we get

[tex]10x=1.6+x[/tex]

[tex]10x-x=1.6[/tex]

[tex]9x=1.6[/tex]

[tex]x=\frac{1.6}{9}[/tex]

[tex]x=\frac{16}{90}[/tex]

[tex]x=\frac{8}{45}[/tex]

Hence, the fraction =[tex]\frac{8}{45}[/tex]