What are the laws in rounding a numbers?

Answer 1

To round a number to a given number of significant figures (digits) or decimal places you need to look at what comes after the appropriate number of digits. If what follows is less than 5 then the number is truncated (chopped off) at the appropriate length. If what follows is greater than 5 then the final digit of the number that is to remain is increased by one and the rest discarded.

So,

1.23456 rounded to 3 significant figures or 2 decimal places is 1.23 since the next digit is 4, which is less than 5.

1.23456 rounded to 5 significant figures or 4 decimal places is 1.2346 since the next digit is 6 which is greater than 5. So 1.2345 is rounded up to 1.2346.

What do you do if the next digit is 5? You look at the next two digits: if they are less than 50 you truncate, if they are greater than 50 you round up the final digit.

Finally, what do you do if the final digit is exactly 5. Many [most] school incorrectly teach pupils to round up from 5. This introduces an upward bias in the results because on average you round down 40 per cent of the times (next digit 1, 2, 3 or 4), and round up 50% (next digit 5, 6, 7, 8 or 9). A better solution is to round up or down so that the new last digit is even. This is the default rounding mode used in IEEE 754 computing functions and operators.