People often have questions involving rounding, especially when

'throwing' away a 5 or 5 followed by zeros. Hopefully this will help.

The question is what to do when you have a number such as 1.85 and

you need to round to the tenth’s place (first decimal place). This

number is exactly halfway between 1.8 and 1.9. Why should one

always round up in such cases? Actually you shouldn’t. If you do

this for several numbers and then use them for something else your

results will be skewed high. Instead we need a rule that will result

in rounding up half the time and rounding down half the time (when

you are doing this to lots of results). How should this be handled?

It depends on whether the last number you are keeping is even or odd.

When you discard an exact 5 or 5 followed by nothing but zeros

two different things can happen to the last digit you KEEP:

1) If the number you are keeping is even you leave it alone and

just get rid of the 5 you are throwing away (round down).

2) If the number you are keeping is odd you round it up (to an

even number).

The easiest way to remember this is the last digit KEPT is

ROUNDED EVEN

Let's say each of the following is rounded to 2 sig fig.

1.45     =>       1.4 (discard the 5 and round even - rounding

                                down in this case)

1.55     =>       1.6 (discard the 5 and round even - rounding

                                 up in this case)

1.6500 =>       1.6 (discard the 500 and round even - rounding

                                down in this case)