Question

Which simplified fraction is equal to 0.17 (7 repeating)

Answer 1

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)

Answer 2

`(8)/(45)`

Explanation:

We are given that

`0.1\bar 7`

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

Let x=
`0.1\bar 7`

Multiply on both side by 10 then we get

`10 x=1.77...`

`10x=1.6+0.1\bar 7`

Substitute the value then we get

`10x=1.6+x`

`10x-x=1.6`

`9x=1.6`

`x=(1.6)/(9)`

`x=(16)/(90)`

`x=(8)/(45)`

Hence, the fraction =
`(8)/(45)`