IM NOT saying 3/3 isn't equal to 1.
If just saying that if 1/3 is .333333...
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answers:
Paul say: 3/3 = 0.99999... where the nines go on forever.
This is numerically the same as 1 (although not necessarily if you get to more advanced maths).
Here's the school leaver explanation.
0.999999... = x
9.999999... = 10x (remember the 9s go on forever so we never run out)
10x-x 9.999999.... - 0.999999....
9x = 9
x = 1.
Here's a video explaining this:
https://www.youtube.com/watch?v=4V5NJiGB...
Here's a more advanced video explaining why 0.999999... isn't necessarily one.
https://www.youtube.com/watch?v=aRUABAUc...
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J say: Every real number which can be written as a finite decimal can also be written as an infinite decimal.
E.g.
0.5 = 0.499999.... (repeat 9's forever)
0.37 = 0.36999.... (repeat 9's forever)
1.0 = 0.999999.... (repeat 9's forever)
Usually one prefers the finite form, the the infinite form is equally correct.
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Norebal say: I know , you are going to get 0.9999 instead of 1
The mistake comes from the fact that 1/3 IS NOT 0.3333. It is a never - ending number that repeats the pattern ( 3 ) , therefore it is not irrational.( That is you disregarded the remainder in the division ).
It would be like dividing 20 by 3 and get 6 with remainder 2. If you disregard the remainder, and multiply only the quotient 6 by 3, you would get 18, not 20.
Now if you divide 1 by 3, you would get 0.3333 and 1/3 of a ten-thousandth. ( Exactly )
If you multiply the answer by 3 : that is 3. ( 0.3333 + 1/3 t.th ) = 0.9999 + 0.0001 = 1
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nbsale say: .999999... IS equal to 1.
x = .999999
10x = 9.999999
Now subtract and get
9x = 9
x = 1