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I am confused with the multiplication rules when it comes to multiply a decimal number with a number like 2. For example, if I want to calculate tidal force between the earth and the moon, I have a bunch of decimal numbers measured before such as mass, distance, radius etc. and there is also a number 2, which comes from the formula, i.e. the derivative of gravitational force (~1/r^2).

Significant figure rules state that I should round the result according to the number with the least number of significant figures. But it is 2 here, and if I apply it, I lose a lot of accuracy in the result.

What do you do in such calculations? Is it Ok to ignore the significance of 2 here?

Thanks

mrq
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  • The 2 in this equation is exact, so it has as many significant figures as you want. – Paul Feb 17 '18 at 19:37

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The rule refers to numbers that appear as a consequence of measures. In general, the $2$ and other exponents that appear in formulas are considered exact, as one usually operates on the assumption that the formula is accurate.

If one is willing to nitpick, one can discuss whether the $2$ in that exponent is really the best we can do, and physicists have measured up to what extent it is a two or not. In most cases the accepted error is very small (say, in 15${\rm th}$ digit) so it is harmless not to consider it.

Martin Argerami
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