Question

Question #cc907

Answer 1

The correct way to add them is by making them rational numbers.

Explanation:

By the way one written by you is not equal to one.
Its more than one.
You should try adding
0.87777777..... and 0.1222222222.... by converting them to rational numbers.
I think it should be equal to one

Answer 2

No.

Explanation:

It would be true if you, for example added `0.1333333...+0.8666666...`

let `x=0.1(3)` and `y=0.8(6)`

`x+y=(10x-x)/9+(10y-y)/9`
`x+y=(1.3(3)-0.1(3))/9+(8.6(6)-0.8(6))/9`
`x+y=1.2/9+7.8/9`
`x+y=(1.2+7.8)/9`
`x+y=9/9=1`

Answer 3

No!
Finding out the exact value of this sum see the explanation

Explanation:

`color(blue)("Consider just "0.12333....)`

Write as `0.123bar3` where `bar3` means it goes on repeating for ever.

Set `x=0.123bar3`

`"Then "color(white)("dd")1000x=123.33bar3`
`ul("Then "color(white)("vdd")100x=color(white)("d")12.33bar3 larr" Subtract"`
`1000x-100x=111.0`

`900x=111`

`color(white)("dd.")x=111/900 = 0.123bar3`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Consider just "0.877bar7)`

Set `x=0.87bar7`

`"Then "100x=87.77bar7`
`ul("Then "color(white)("d")10x=color(white)("d")8.77bar7larr" Subtract")`
`100x-10x=79.0`

`90x=79`

`x=79/90`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

`79/90+111/900`

`[79/90color(red)(xx1)]+111/900`

`[79/90color(red)(xx10/10)]+111/900`

`color(white)("ddd")790/900color(white)("ddd")+111/900color(white)("d")= color(white)("d")901/900`

`color(white)("dddddddddddddddd")->color(white)("d")1+1/900`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Conclusion")`

`0.123bar3+0.877bar7 !=1`

Where `!=` 'means not equal to'