Why are constants considered to have an unlimited number of significant figures in calculations with measured values?

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  • Dr W
    Lv 7
    1 month ago

    you're mistaken.  it's "exact numbers" that have infinite sig figs.  like 1000mg = 1g.  By definition those numbers 1000 and 1 are exact numbers.

    the idea is that "sig figs" is a quick and dirty way to estimate imprecision in a number.  And sig figs is based on the rightmost digit having imprecision of +/- 1.

    .. 100.15g = 100.15g +/- 0.01g

    .. 324 miles = 324 +/- 1 mile

    .. 6.02x10^23 = (6.02 +/-.0.01) x 10^23

    but if we count out exactly 5 baseballs

    .. 5 +/- 0 baseball

    is an exact number.  It has the same value as

    .. 5.0000000000000000000000000 +/- 0.0000000000000000000000001

    .. baseballs

    and the same value as 

    .. 5.infinity zeros +/- infinite zeros then 1

    which has infinite sig figs

    **********

    remember these...

    .. (1) all exact conversion #'s have infinite sig figs

    .. (2) any "constants" that you look up need to have AT LEAST as many 

    .. . . .sig figs as the numbers given in the problem statement, preferentially 1 EXTRA

    .. . . .this forces the sig figs in the result to be limited to the sig figs in the problem

    .. .. .rather than the sig figs in your choice of constants

    examples

    .. (1) convert 20.040g to kg

    .. . . 20.040g * (1kg / 1000g) = 0.020040 kg (with 5 sig figs)

    .. .. .in this case, 20.040 has 5 sig figs, 1 is exact and 1000 is exact

    .. (2) convert 2.000 moles H2 to molecules H2

    .. . . 2.000 mol * (6.02x10^23 molecules / mol) = 1.20x10^24 molecules

    . . . .note that although my 2.000 has 4 sig figs, my choice of "constant"

    .. . . only had 3 sig figs which limited the answer to 3 sig figs.. This is a PROBLEM.

    ..  .. t's like saying.. NO TEACHER.  I'm not converting 2.000mol.  I choose to convert

    .. . . 2.00 mole H2 to molecules H2.  Don't make this mistake!

    . .   it's equivalent to peeing on the teachers leg. 

    . (3) convert 2.000 mole H2 to molecules H2... the RIGHT WAY

    ... . 2.000 mols * (6.0221 x 10^23 molecules / mol) = 1.204x10^24 molecules

    ..   .in this case, the number I'm converting FROM has 4 sig figs.  So I choose

    .. .. my constant value to have 5 sig figs

  • 1 month ago

    What constants are you talking about? Many of the constants that I think about do not have unlimited significant figures, but many are known very accurately. So, Avogadro's number is commonly stated as 6.02X10^23, but in Wikipedia, it is given as 6.02214076×10^23 mol−1. The speed of light is 299 792 458 m / s which has 9 significant digits, but this is not unlimited. 

    Now, some conversions and equivalences like 12 inches/1 foot or 1000 m/1 km do have unlimited significant figures because these are defined to be exact. 

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