Hey, when we solve for significant figures, why do we completely get rid of the remaining decimals even though hey have more accurate information?
Ex. 1.23*4.84=5.9532 but we would make it 5.95 based on Sig figs, even though those last two decimals are closer to the answer. Why is this? I know it’s less accurate, though it seems like we’re losing valuable accuracy (even if it’s not perfect, it should be closer)
In: Mathematics
What I think a lot of the answers you’re getting have touched on, but maybe not stated explicitly, is the idea that the extra digits would convey a *false* sense of precision. Every measurement we make also has errors involved.
Let’s use your example, in a classic setting I would give to students. You have a rectangle and want to get its area by measuring the width of two sides using a ruler. In truth, your ruler has an accuracy of +/- 0.005, you can roughly tell whether the edge is closer to 1.23 or 1.24 but no more than that.
Based on this, you know that the area must be between (1.225 * 4.835 = 5.922875) and (1.235 * 4.845 = 5.983575) or (5.95 +/- 0.03) which shows how errors compound. Attaching more digits to the end accomplishes nothing, you can’t make the result more accurate.
However, attaching those extra digits can create the impression that you have a more precise result than you really do. Again, using your numbers, if we multiplied (1.2300 * 4.8400 = 5.9532) then it looks like those zeroes aren’t doing anything, but they are. Those zeroes tell us that our ruler is accurate to within +/- 0.00005 and that the result is actually between (5.9528) and (5.9535) which is far more precise than when we only knew two digits to the right of the decimal.
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