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'