*By Mojo*

This happened awhile ago but a) demonstrates by extreme preoccupation with the accuracy of other people’s statements and b) my tenacity in arguing points when I know I am right. I feel these aspects of my personality are important for me to pass on to you lest you get the impression that I’m a jerk. I’m not… I just have a lot of pet peeves. Also, this story is hilarious and demonstrates the type of people I work with.

There I sat, working away at my station and chatting with my boss when the topic arose about how terrible the education system has become. The example he used was that his eldest daughter was erroneously corrected for rounding a number DOWN when it ended in five instead of up. For example, when asked to round the numbers 0.35 0.45, and 0.55 to the nearest tenth, she worked out the answer to be 0.4, 0.4 and 0.6. In other words, she would alternate between rounding up and rounding down when the next number was a 5 depending on if the number in front of it was even or odd. Her teacher supposedly attempted to curb this behavior citing it as incorrect but, in my coworker’s opinion, it was indeed the correct method.

I, having never heard of this technique before, immediately assumed he was wrong. It sounded crazy. Why the hell would it matter if the number ahead of it was odd or even? Well turns out, I was wrong. That’s right faithful readers. Mojo was wrong about something. But all was not lost. The universe balanced itself out when a second coworker entered the fray half-way through the conversation.

To back up a bit however, a quick Google search uncovered something called asymmetric rounding which actually introduces a significant amount of bias when rounding long lists of numbers. Of course the very act of rounding introduces error but this compounds it. There are several methods for eliminating this asymmetry and, as it turns out, my boss’s daughter was employing a single technique known as unbiased rounding, convergent rounding, statistician’s rounding, Dutch rounding, Gaussian rounding, or bankers’ rounding.

As I explained this to my boss (who was himself unsure of the exact reason for the odd/even rounding and wanted me to help clarify in case he has to explain this to his daughter’s teacher), another co-worker arrived on the scene and decided to throw his two cents in about the utility of rounding in general. In his opinion, he saw rounding as merely the act of human laziness when dealing with large strings of numbers after a decimal place. He used two main examples in an attempt to get his point across: 1) Pi is reduced to 3.14 on many occasions despite, as we all know, being a much longer string of numbers; and 2) When taxes are added to the prices of items the price is actually different from the mathematical result of the addition but rounding is used to make the price more manageable for consumers/vendors.

The argument itself is moot since even if true (which it isn’t) the usefulness of rounding would still be present. In fact, the number pi is a very good example of the OPPOSITE point he was trying to make. If not for rounding, pi (and radical or irrational numbers) would be completely unmanageable. Pi is infinite. Expressing that number completely has never been done to date. Clearly, in this case, rounding is far from an exercise in laziness. It is downright necessary.

But to this person’s credit, maybe that was his point. It’s not that it is entirely useless but it changes the number itself which decreases the accuracy of the result. This must is true. However, when dealing with accuracy, there are times when rounding is absolutely necessary. The accuracy of your result in any mathematical operation must only be as accurate as the initial measurements or numbers you began with. If you have a scale that can only display weights to the nearest 1000th then any result you obtain from the use of measurements obtained MUST be rounded to that same amount of decimal places. Otherwise you are fabricating your result beyond what you can actually measure with the instruments at hand. In these cases, rounding actually INCREASES the accuracy, veracity and honesty of your results.

All of these points were made clear to this individual by me but unfortunately fell on deaf ears. I was accused of not listening and not understanding which eventually lead to me being accused of yelling.

Well at least that part of what he was saying, at that point, was accurate. :)

Thanks for reading!!

Or use fractions?

I was JUST talking to someone about a similar experience with this when I got into an argument with my highschool chemistry teacher over this. And to my surprise, no one believed me that you should round down on exactly .5. I always thought this was basic when significant figures were taught.

Hmm, rounding up or down on .5 is tricky.

It’s easier when there’s another decimal behind it, because then it makes more sense: .49 rounds down, .51 rounds up. But .50 is smack in the middle, so if you encounter it often when adding numbers, it’s better to alternate between rounding up and down to counter the error that you introduce (2 x 0.5 is after all exactly 1).

But personally, I usually do the adding & substracting first, then when I have the result, finish with the rounding. That way, you’re not combining rounding errors, there’s only one rounding.

Depending on how many significant digits/figures you have:

1.49 rounds to either 1 or 1.5

1.51 rounds to either 1.5 or 2

1.50 rounds to either 1.5 or 2

In 1.49, the 9 is irrelevant in rounding down to 1 (that is, if you have one significant digit/figure). The 4 is relevant because it’s the adjacent number. The 9 is relevant in rounding up to 1.5, but only if you have two significant digits/figures.

If you get the number 1.50 and only two digits/figures are significant, you’re left with 1.5. If you have 3 significant figures, it stays 1.50. If you only have one, it rounds up to 2 as per convention.

“

If you only have one, it rounds up to 2 as per convention.”Unless, as mentioned before, you’re rounding a whole string of numbers. For the sake of precision, it does make more sense to alternate in that case. I hadn’t actually heard of it myself, but I can see the logic.

Of course, the teacher was right and the colleages daughter was wrong, as the assignment was most llikely to round a series of one-off numbers, not a bunch of numbers you would still add up afterwards.

That’s what I meant. Using the rounding convention Mojo described (odd/even alternation), 1.5 in a string would round up because 1 is odd.

I see, bad example then :)

1.5 would round up to two anyway, as per convention, because 0, 1, 2, 3 and 4 round down, 5, 6, 7, 8 and 9 round up. 2.5 would round up too.

Mojo’s rules are very specific to large amounts of numbers that need further calculations done with them afterwards (statistics, etc…). 2.5 would round down in that case.

The exercise the teacher gave wasn’t one of those situations.