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Math Help - Units

  1. #1
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    Units

    100.0 g x 1.00 cal/g x Celcius x 28.6 degrees celcuis


    I need to multiply all of these and use significant numbers.
    I think the number would be 3000, but how do I label it?
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  2. #2
    Super Member Aryth's Avatar
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    First, we should have it in a way that is visually easier to understand:

    (100.0g)\left(1.00\frac{cal}{g*Celsius}\right)(28.  6 \ Celsius)

    We first multiply the first two terms in the analysis:

    \left(100.\frac{cal}{Celsius}\right)(28.6 \ Celsius)

    Notice that the 100.0 lost it's 0 because 1.00 has 3 significant digits and therefore 100 also has to have three sig digs, since 100.0 has 4 significant digits, then we keep the decimal and lose the zero to get 3 significant digits. Now we multiply the other two numbers:

    \left(100.\frac{cal}{Celsius}\right)(28.6 \ Celsius) = 2860 \ cal

    You can use 2860 because both 100. and 28.6 have 3 significant digits, and 2860 has 3 as well, therefore the answer works.
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