## If last digit is 5: round to nearest even number?

Hannah Chew 2A
Posts: 76
Joined: Fri Sep 29, 2017 7:05 am
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### If last digit is 5: round to nearest even number?

"IF LAST DIGIT IS 5: ROUND TO NEAREST EVEN NUMBER
(2 sf then 2.35 is 2.4 and 2.65 is 2.6)"

I was reading through the "Everything You Want to Know about Sig Figs" link on the class website, and I read the part above. I've never heard of this rule and have been sticking to the 0-4, round down, and 5+ round up rule. Is there a reason why we round to the nearest even number when the last digit is 5 and are we expected to follow this rule always? Thanks in advance!

Kyle Reidy 3H
Posts: 19
Joined: Fri Sep 29, 2017 7:06 am

### Re: If last digit is 5: round to nearest even number?

The reason we do this is so that we introduce less error when we round numbers. 5 is not closer to 10 than it is to 0, and it is only by convention that most people round 5 up to 10. However, this means that every number you round in this way would be slightly over the real value and your data will be skewed to larger than it should be. On the other hand, if you were to always round 5 to 0, your data would be skewed smaller. We round to the nearest even number in the hopes that we will have some overestimates and some underestimates which will cancel each other out.

For example, say we wanted the result of:
2.5 + 7.5 + 1.0 + 9.2 + 4.5 + 6.8
The actual result here is 31.5.
By "conventional" rounding methods, we would get:
3 + 8 + 1 + 9 + 5 + 7 = 33
Using our "round to even" method, we instead get:
2 + 8 + 1 + 9 + 4 + 7 = 31
which is closer to the actual result.

Clara Rehmann 1K
Posts: 53
Joined: Fri Sep 29, 2017 7:03 am

### Re: If last digit is 5: round to nearest even number?

Rounding to the nearest even number (eg. 2.5 -> 2, 5.5 -> 6) prevents there from being a significant shift up in the quantities you have. If you always always always round 5 up, especially with a big data set, you'll end up with the average of all your numbers being shifted up. Rounding to the nearest even makes it more 50/50 and keeps the average error from shifting up. This site has a pretty good explanation if my words didn't make any sense: https://mathematica.stackexchange.com/questions/2116/why-round-to-even-integers