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Johnathan
Lv 7
Johnathan asked in Science & MathematicsMathematics · 5 years ago

How would the repeating decimal 0.9999999999... be expressed as a fraction?

It looks like it would be equal to 1, but that can't be right...

5 Answers

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  • Demiurge42
    Lv 7
    5 years ago

    0.9 with the 9 repeating is equal to 1. 1 isn't a fraction though. You can make it a fraction in many ways. 1/1 works or 2/2 and infinitely more.

  • hayharbr
    Lv 7
    5 years ago

    It is equal to 1. If you call it x = 0.999999999... then multiply both sides by 10 you get

    10x = 9.999999... and now subtract the original call:

    - x   =-0.999999..

    You get 9x = 9.000000000... so 9x = 9 making x = 1.

  • Roger the Mole
    Lv 7
    5 years ago

    Yes, 1 is correct. To prove it:

    Let x = 0.999999...

    10x = 9.99999... = 9 + x

    Subtract x from both sides:

    9x = 9

    x = 1

  • οικος
    Lv 7
    5 years ago

    This reminds me of the problem posed to a scientist and an engineer. It goes: A naked man and a naked woman stand at opposite ends of a room. Every five seconds, they halve the distance between them. To the scientist, they never meet. To the engineer, "They get close enough for all practical purposes.". Follow the engineer here and round off to one.

  • Captain Matticus, LandPiratesInc
    Lv 7
    5 years ago

    But it is, and you know it.

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