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# Rounding Numbers

By June 7, 2013

Here are three helpful hints if you are trying to help somebody to round numbers:

1.  When the first digit dropped is less than 5, do not change the preceding digit.   E.g., 2.324 rounded off to the nearest hundredth is 2.32.

2.  When the first digit dropped is greater than 5, or 5 followed by one or more non-zero digits, increase the preceding digit by one.
E.g., 2.316 and 2.3151 are both 2.32 when rounded off to the nearest hundredth.

3.  When the first digit dropped is 5 and there are no digits following or the digits following are zeros, make the preceding digit even (i.e. round off to the nearest even digit).  E.g., 2.315 and 2.325 are both 2.32 when rounded off to the nearest hundredth.

Note: The rationale for the third rule is that approximately half of the time the number will be rounded up and the other half of the time it will be rounded down.

June 13, 2013 at 9:17 am
(1) Five Triangles says:

Rule 3 is not universally followed.

4 down, 5 up is far simpler and more sensible

June 14, 2013 at 1:59 pm
(2) Sten-Åke says:

Joe, i would not say it is “wrong”. It is a concistent method and the number is still approximated by one of the two closest numbers with that precision. It is just one more way of rounding. And rule 3 could be used by statisticans that want to change the average as little as possible.

June 17, 2013 at 3:42 am
(3) Elaine says:

My Scottish primary education said greater than 5 – up, less than 5 down. A version of Rule 3 was followed if the round off figure was 5 – look to the next figure – 5 or more round up, less than 5 round down. The rationale was that you would be likely to be right at least half the time.

So 2.357 goes to 2.4, 2.352 goes to 2.3.

Nowadays we teach it more simply here. We say – 5 or more round up, less than 5 round down so both the examples above would go to 2.4.

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