For numerical calculations, the accuracy obtained from solution of
problem generally can never be better than the accuracy of the problem data.
This is what is to be expected, but often handheld calculators or computer
involve more figures in the answer than the number of significant figures used
for the data. For this reason, a calculated result should always be
"rounded off" to an appropriate number of significant figures.
To convey appropriate accuracy, the following rules for rounding
off a number to n significant figures apply:
- If the n + 4 digit is less than 5, n + 1 digit and other following it are dropped. For example, 2.326 and 0.451 rounded to n = 2, significant figures would be 2.3 and 4.5.
- If n + 1 digit is equal to 5 with zero following it, then round off the nth digit to an even number. For example, 1.245 and 0.8655 rounded to n = 3 significant figures become 1.24 and 0.866.
- If the n + 1 digit is greater than 5 or equal to 5 with any nonzero digits following it, increase the nth digit by 1 and drop n + 1 digits and other following it. For example, 0.723 87 and 565.500 3 rounded off to n = 3 significant figures become 0.724 and 566.
