math

I always thought I understood significant figures...until I attempted to tutor someone. Some of the rules seem counterintuitive. For instance...
10.070 why is it 5 sig fig's? the "0" on the right is useless. without it the # holds the same value.
20 Why is it only "1" sig fig? the "zero" is the difference between two and twenty. seems pretty sig to me.
0.01234 has "4" sig fig's. why isn't the zero to the right of the decimal sig? without it, the # doesn't hold the same value...can someone please explain the concept that I'm missing??

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  1. <<10.070 why is it 5 sig fig's? the "0" on the right is useless.>>
    The fact that the zero is there beyond the decimal point means that it IS a significant figure.

    <<20.: Why is it only "1" sig fig? the "zero" is the difference between two and twenty.>>
    I agree. With a decimal point after the 20, it should be clear that the number is closer to 20 than 19 or 21. Therefore there are two sig figs. However, if they had just written 20 without a decimal point, then that would be one significant figure. For example: 2000 with no decimal has only one sig fig. also.

    <<0.01234 has "4" sig fig's. why isn't the zero to the right of the decimal sig?>>
    Until you get a nonzero number on the left side, none of the figures are significant in terms of precision; they just establish the order of magnitude. Think of writing it as 1.234*10^-2. The exponent -2. does not establish the precision, only the 1.234 does.

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