How to Round-Off

Round-off

Round-off errors arise because it is impossible to represent all real numbersexactly on a finite-state machine (which is what all practical digital computers are).

All non-zero digits are considered significant. For example, 91 has two significant figures (9 and 1), while 123.45 has five significant figures (1, 2, 3, 4 and 5).

CASE A: In rounding off numbers, the last figure kept should beunchanged if the first figure dropped is less than 5.	For example, if only one decimal is to be kept, then 6.422 becomes 6.4.
CASE B: In rounding off numbers, the last figure kept should beincreased by 1 if the first figure dropped is greater than 5.	For example, if only two decimals are to be kept, then 6.4872 becomes 6.49. Similarly, 6.997 becomes 7.00.
CASE C: In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should be unchanged if that last figure is even.	For example, if only one decimal is to be kept, then 6.6500 becomes 6.6. For example, if only two decimals are to be kept, then 7.485 becomes 7.48.
CASE D: In rounding off numbers, if the first figure dropped is 5, and all the figures following the five are zero or if there are no figures after the 5, then the last figure kept should be increased by 1 if that last figure is odd.	For example, if only two decimals are to be kept, then 6.755000 becomes 6.76. For example, if only two decimals are to be kept, 8.995 becomes 9.00.
CASE E: In rounding off numbers, if the first figure dropped is 5, and there are any figures following the five that arenotzero, then the last figure kept should be increased by 1.	For example, if only one decimal is to be kept, then 6.6501 becomes 6.7. For example, if only two decimals are to be kept, then 7.4852007 becomes 7.49.