Question about significant figures and fractions
Perhaps a simple question, but I can't find an answer.
Do 1/3 have the same number of significant figures as 0.333...?
On one hand, they're the same number and therefore must have the same number of significant figures.
But on the other hand, both 1 and 3 are only exact to the nearest whole number and might not be equal to exactly 1.000... or 3.000... respectively. One could argue that the result of 1/3 still only have one significant figure and should therefore equal 0.3.
Any thought on this?
2 replies
1/3 and 0.333… are mathematically identical. Imprecision is only introduced when when you approximate 0.333…, either by standard rounding or using floating point.
Very relatedly, 1 and 0.999… are also mathematically identical.
Well, 1 and 3 are whole numbers, and 1/3 is fully complete and accurate as is, thus sig figs simply dont apply. When you jump to a decimal approximation (0.3333333...), or a measurement, you're introducing some amount of error or imprecision, and sig figs start to enter the picture.