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
Two things:
1. 1.23 x 4.84=5.9532 should only be taken to five significant figures if the first two numbers are also accurate to more than five significant figures. So it’s 1.23000 x 4.84000. If the first two are only stated to three significant figures you can’t, or shouldn’t, assume the values are accurate to an additional significant figures. If the first values were actually 1.2349 and 4.8449 but rounded to the values you state then the answer would be 5.9830. Even taking the answer to three significant figures is a bit generous…
2. Even when you do know the answer to many significant figures past a point the increased accuracy starts to lose value. For example NASA uses a value of Pi to 15 decimal places, even though it is known to trillions of decimal places. This is because 15 decimal places is enough to plot a billions of miles long space flight to within a couple of inches, and by then the error bars for other factors are much larger than the course projection errors.
Latest Answers