# can someone explain this math question?

ok so 1/3=.33 repeating so .33.......*3=.99........

1/3*3=1

.99 does not equal one

yes i know that 3/3=1

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the infinite series 9/10 + 9/100 + 9/1000 ..... = 0.999.... does equal 1.

let S = 0.9999..........

then 10S = 9.99999..........

subtract the equations

9S = 9.00000........

S = 1

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• OK

1/3 = .333 and the 3 repeats forever. So to show this truly accurately you need to either show the 3's repeating on and on or you could decide to stop the 3 (let's after three places and show this:

1/3 = .333 1/3

Now when you multiply 1/3 x3 = 1

.333 1/3 x 3 = .999 + 0001/3 3 times or .001

= 1

So you see, as stated above, .999999 repeating does really equal 1 or, because the 3 repeats forever, at some point, it approaches 1 when it is added to other repeating 3s.

Hope this helps.

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• To say that mathematicians have "proved" 0.99.... = 1 gives the impression that it was ever an open question.

It's important to realize that 0.99... is a symbol which refers to a number.

People are so used to seeing decimals represent numbers which are not whole, and are so committed to the fallacious idea that every number has only one decimal symbol representation.

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• .9999 repeating represents 1 in our Mathematical system; which is just a system that we, as humans, developed to help explain the world around us, this is only base 10 mathematics. There is so much we do not know. Mathematics makes assumption; We do this because it is necessary to explain the world around us. It is just another "language."

Source(s): I'm a professional nerd. Oh, and All American Mathlete 1984
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• Mathematicians have proved that 0.999999 repeating is equal to 1, try a google search to find the proofs.

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• You answered it yourself. The math doesn't lie. For example:

1/9 = 0.1111.....

Let's have x = 0.1111.... = 1/9

x * 9 = 1 because 1/9 * 9 = 1

Therefore 0.1111.... * 9 must = 1

Therefore 0.9999.... = 1

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