3rd Grade math - Rounding?

[Russ Filtz]

Was checking my 3rd graders math homework and spotted an error (at least in every math course I remember from my engineering degree). They are teaching to round UP every time you have a "5"! So a 4.5 rounded would be 5, and 45 rounded would be 50. Absolutely wrong from an engineering standpoint. We are taught to round to the EVEN number. So 4.5 would be 4, not 5. That way "statistically" speaking, you aren't always rounding in one direction thereby creating even more errors. Of course, even us engineers take liberties sometimes with the concept and round to the odd number on a "5". IF it makes the calculation more conservative.

Not a huge deal I guess. Maybe it's easier to teach the concept of rounding first, and then teach it the right way later for 3rd grade brains? Any teachers out there that know the theory? Drives me insane thought, thinking it's easier to just teach the "right" way in the first place.

[David Epperson]

During my engineering studies I never heard of "rounding to the even" number. Always to the next whole significant digit. 0.45 would round to either 0 or 0.5 never to 0.4.

[Rob Russell]

What David said.

[Greg Peterson]

I'm no math whiz, but I did stay in a Holiday Express last night. I vote for round to the nearest significant digit.

[glenn bradley]

What David said again. Round to the nearest larger whole number.

[Greg Cuetara]

It all depends on how much precision and accuracy you want. If the directions state to round 4.5 to the nearest whole number then that would be 5. If you had 4.4 then the nearest whole number would be 4. In engineering if you round it should always be up...if you come out with needing 4.1 bolts then you have to round up to 5 because there is no way that you can get .1 bolts and 4 bolts will not satisfy your requirements.

[Russ Filtz]

Not talking sig figs, but after review, it seems like rounding up all the time IS the method being taught now. In my method 4.5 rounded to integers would be 4. 5.5 would be 6. 6.5 would still be 6, etc. 1.45 rounded to tenths would be 1.4, not 1.5 as being taught now.

Whoever taught me the round to even method stated it would tend to even out cumulative errors in a chain of calculations. Google searches show the round up with "5" approach, but no real reasoning behind it other than convention.

[Cliff Rohrabacher]

When doing quick calc's in my head I round up and down and it all sort of evens out. The answer I get isn't accurate but it's plenty close for horseshoes.

[Mike Henderson]

I was taught that a "5" in the rounding position caused the adjacent digit to go up by one. So 4.5 rounds to 5, 45 rounds to 50, etc.

Anything less than 5 in the rounding digit does not cause the adjacent digit to go up by one. So 4.4 is rounded to 4.0 and 44 is rounded to 40.

I guess you can think of it that there are five digits that cause rounding up and five that do not. The five that do not are 0, 1, 2, 3, and 4. The five that do cause rounding up are 5, 6, 7, 8, and 9.

So there are equal probabilities of going either way, which makes it fair (or makes it even out).

Mike

[Russ Filtz]

Although rounding up may be convention now. May not have always been the case! Found this on various websites.

"1. Some statisticians prefer to round 5 to the nearest even number. As a result, about half of the time 5 will be rounded up, and about half of the time it will be rounded down. In this way, 26.5 rounded to the nearest even number would be 26—it would be rounded down. And, 77.5 rounded to the nearest even number would be 78—it would be rounded up."

http://en.wikipedia.org/wiki/Roundin...to-even_method
"The Round-to-even method has been the ASTM (E-29) standard since 1940. The origin of the terms unbiased rounding and statistician's rounding are fairly self-explanatory. In the 1906 4th edition of Probability and Theory of Errors [1] Robert Woodward called this "the computer's rule" indicating that it was then in common use by human computers who calculated mathematical tables. Churchill Eisenhart's 1947 paper "Effects of Rounding or Grouping Data" (in Selected Techniques of Statistical Analysis, McGrawHill, 1947, Eisenhart, Hastay, and Wallis, editors) indicated that the practice was already "well established" in data analysis."

[Chris Kennedy]

I remember learning the idea of rounding to the nearest even on a 5 when I was taking high school chemistry and physics, but in my math classes, we were always supposed to round up.

I can tell you mathematically speaking that the idea of rounding up _measurements_ to the nearest even is flawed. When you are rounding, you are losing a degree of accuracy/precision (I always forget which one is which), or more to the point, you are saying that you don't have that degree. So, when you round 45.4 to 45, you are really saying that the measured quantity is 45 within a margin of error -- you cannot say with certainty what the next digit is.

So, in particular, you round 45.0, 45.1, 45.2, 45.3, and 45.4 to 45, which is actually 45 plus some unknown error, so in particular, you cannot say it is 45.0. The point being, you are actually rounding 45.0 to 45 (with a margin of error). You round up 45.5, 45.6, 45.7, 45.8, 45.9 to 46 for the same reason. Hence, you round down on 5 digits and you round up on 5 digits and round the same number of times up as down.

The thing is that scientists and engineers may not view rounding 45.0 to 45 as actual rounding (it depends on whether you think it is 45 or 45 plus a margin of error), which is where the idea to round to the nearest even came from.

Cheers,

Chris

[Kevin L. Pauba]

I also have an engineering degree (mechanical) and we were taught like you were, round to the nearest even number. And I too get frustrated by some of the ways my kids have been taught but, so far, they're doing OK. I figure if one of the remaining not in college decide on the engineering path (unlikely, ), they'll relearn it.

[Russ Filtz]

IYou round up 45.5, 45.6, 45.7, 45.8, 45.9 to 46 for the same reason. Hence, you round down on 5 digits and you round up on 5 digits and round the same number of times up as down.

The thing is that scientists and engineers may not view rounding 45.0 to 45 as actual rounding (it depends on whether you think it is 45 or 45 plus a margin of error), which is where the idea to round to the nearest even came from.

Cheers,

Chris

I think that whole round down 5, round up 5 argument is flawed. why would you include 45.0 and NOT 46.0? Therefore you're now rounding down 5 numbers and up SIX numbers if you include 46.0! Sounds like a made up argument to legitimize the rounding method.

[Tom Veatch]

why would you include 45.0 and NOT 46.0?

Because you've already counted the "round on zero" sample with "45.0". Including "46.0" would effectively be counting the same sample twice and would skew the statistics.

As far as "round to even" goes, put another mark in the "That's the way I learned it." column.

[Ben Rafael]

For finances, Mike's way is the standard since things will average out over time. It is the standard in, AFAIK, the financial industry. I believe that method is the way computers round off also.
Mathematicians, generally, use the rounding method called "whatever makes my life easier", that is, when mathematicians actually compute figures. Most mathematics is theoretical and doesn't involve a lot of computations. The computations come in to play when engineers and programmers apply what the mathematicians have produced.