Question #cc907

3 Answers
Jan 16, 2018

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

Jan 16, 2018

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

Jan 16, 2018

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'