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Math Help - orders of magnitude

  1. #1
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    orders of magnitude

    This question is not for a homework assignment.. It's just something that has really been bugging me


    If I was to decrease the number 125,278,840 by two orders of magnitude

    would I simply divide it by 100?

    I've read somewhere that in order to increase a number by two orders of magnitude you multiply by 100


    Thanks for your help!
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    Quote Originally Posted by xcelxp View Post
    If I was to decrease the number 125,278,840 by two orders of magnitude

    would I simply divide it by 100?
    Yes, assuming you are scaling by 10. In general, to increase a number by n orders of magnitude, multiply by 10^n. In this case we have 10^{-2}=\frac1{100}.

    Why does this make sense? The order of magnitude of a number is basically the largest power of ten that is less than the number. 125\,278\,840 is on the order of 10^8 (its order of magnitude is 8), and to decrease it by two orders of magnitude would make it on the order of 10^6. Dividing by 10^2=100 accomplishes this.
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