What is the smallest and largest whole numbers that round off 80000 to the nearest thousand?

Answer 1

Smallest: 79500

Largest: 80500

Although many schools teach you to round 5 up, the IEEE (Institute of Electronic and Electrical Engineers) standard 754 is to round up or down so that the new "last" digit is even. See link for more.

The problem with always rounding up from 5 (or more is that it introduces an upward bias. Thus,

If the number is 0.0 you don't need to round

If the number is 0.1, 0.2, 0.3 or 0.4 you round down

If the number is 0.5, 0.6, 0.7, 0.8 or 0.9 you round up

So for a random last digit, 5 times out of 10 you round up and 4 times out of 10n you round down: (and one out of ten is no change). The net result is an upward bias

One possible solution is to round up from 0.5 half the time, round down the other half. That satisfies the bias problem but introduces another - that of reproducibility. If someone else were to look at your data would they round up/down the same way you did? Unlikely. You need a system which will round 0.5 up half the time and down half the time but where the decision is made for you.

Hence the best solution is the answer given above: Round up or down so that the new last digit is even. See link for more.