/ 2.0012 ≈ 4.3 2 × 0.8 ≈ 2 If, in the above, the numbers are assumed to be measurements (and therefore probably inexact) then "8" above represents an inexact measurement with only one significant digit. Therefore, the result of is rounded to a result with only one significant digit, i.e., instead of the unrounded "64" that one might expect. In many cases, the rounded result is less accurate than the non-rounded result; a measurement of "8" has an actual underlying quantity between 7.5 and 8.5. The true square would be in the range between 56.25 and 72.25. So is the best one can give, as other possible answers give a false sense of accuracy. Further, the is itself confusing (as it might be considered to imply , which is over-optimistic; more accurate would be ). Addition and subtraction using significance arithmetic When adding or subtracting using significant figures rules, results are rounded to the position of the least significant digit in the most uncertain of the numbers being added (or subtracted). That is, the result is rounded to the last digit that is significant in each of the numbers being summed. Here the position of the significant figures is important, but the quantity of significant figures is irrelevant. Some examples using these rules are: {|cellspacing=0 cellpadding=2px | || || ||1 |- |style="border-bottom: 1px solid black;"|+ ||style="border-bottom: 1px solid black;"| ||style="border-bottom: 1px solid black;"| ||style="border-bottom: 1px solid black;"|1.1 |- | || || ||2 |} 1 is significant to the ones place, 1.1 is significant to the tenths place. Of the two, the least precise is the ones place. The answer cannot have any significant figures past the ones place. {|cellspacing=0 cellpadding=2px | || || ||1.0 |- |style="border-bottom: 1px solid black;"|+ ||style="border-bottom: 1px solid black;"| ||style="border-bottom: 1px solid black;"| ||style="border-bottom: 1px solid black;"|1.1 |- | || || ||2.1 |} 1.0 and 1.1 are significant to the tenths place, so the answer will also have a number in the tenths place. {|cellspacing=0 cellpadding=2px style=text-align:right | || || ||9.9 |- | || || ||9.9 |- | || || ||9.9 |- | || || ||9.9 |- | || || ||3.3 |- |style="border-bottom: 1px solid black;"|+ ||style="border-bottom: 1px solid black;"| ||style="border-bottom: 1px solid black;"| ||style="border-bottom: 1px solid black;" |1.1 |- | || || ||40.0 |} All the addends are significant to the tenths place, so the answer is significant to the tenth place. While each