Name: Linda T.
Why is 1 is equal to .99999 (repeating)?
Would you agree that if a - b = 0, then a = b? Then think of what it means to subtract .999... from 1. What you get is 0.000...1, with the "0" repeating infinitely before you get to that final 1. In other words, you never get to the final 1! So, since 1 - 0.999... = 0, 1 and 0.999... must represent the same number.
Richard E. Barrans Jr., Ph.D.
PG Research Foundation, Darien, Illinois
Oh, this is one of those "classic" algebra problems, sort of like math trivial pursuits.
let x = 0.999999.... forever
then 10x = 9.9999999...... forever
then 10x minus x = 9.99999.... minus 0.99999....
which equals exactly 9
so 10x -x = 9x
and 10x-x = 9
so 9x = 9
x = 1
Just sort of a cute thing with math.
Think about subtracting one from the other:
1-.9=0.1, 1-.999=0.001, 1-.9999999999=0.0000000001, and so on.
If the nines never end, the zeros never end. The difference is actually zero. If The difference is zero, the numbers are equal.
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012