Question

Question #11b39

Answer 1

`223/99` & `2 25/99`

Explanation:

Let `x =2.bar(25)`
Then, `100x=2.bar(25)*100=225.bar(25`

Subtracting (1) from (2),
`100x-x=25.bar(25)-225.bar(25`
`99x=223`
`x=223/99`

As mixed fraction,
`99 |bar(223)|2`
`" "|198`
`" "|bar("25 ")`

`=2 25/99`

Answer 2

`223/99 color(white)("d") ->color(white)("d") 2 25/99`

Explanation:

The trick with these to generate another equation that you can subtract from the first to eliminate the repeating decimal.

Set `x=2.252525...`

we need to generate from this a value that has the 2 as the first decimal place.

Then `100x=225.252525....`

So

`100x-x=225.252525...`
`color(white)("dddddddddd")ul(color(white)(22)2.252525...)larr" Subtract"`
`color(white)("dddddddddd")223`

`100x-x=223`

`x(100-1)=223`

`x=223/99 color(white)("d") ->color(white)("d") 2 25/99`