Proving 0.999… is 1

Did you know that 0.99999 (repeating) is the same number as 1? Here’s a simple proof:

  1. Let a = 0.9999…
  2. Multiply by 10: 10 * a = 10 * 0.9999…
  3. Simplified: 10a = 9.999…
  4. Subtract a: 10a – a = 9.999… – 0.9999…
  5. Which means: 9a = 9
  6. Divide 9: a = 1
  7. Voila: 0.9999… = 1

Of course, there’s always the simpler:

  1. 1/3 = 0.3333…
  2. Multiply by 3: 1 = 0.9999…

From Slashdot.

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One Comment

  1. Posted October 21, 2010 at 4:36 pm | Permalink

    The magic of “Related posts” shows me that I was fascinated by this exact thing 4 years ago.

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