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# Does 0.5 round up or down?

Round up or down so that the new last digit is even.

Rationale:

Some people advise you to round up 0.5 others say round down. The problem with that approach is as follows:

In the first case

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 4 downs and 5 ups (and one no change).

Net Result: you introduce an upward bias.

In the second scenario, you introduce a downward bias through rounding.

Possible solution:

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.

Long and a bit roundabout but it should satisfy not only the mathematicians but the statisticians and pedants as well. Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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