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Nitya Nigam Rounding numbers is a concept you were probably taught in primary school. The rule generally told to 7-year-olds is that numbers ending in 1-4 are rounded down, while numbers ending in 5-9 are rounded up (numbers ending in 0 aren’t rounded at all). This is a bit of an arbitrary rule - there are 9 numbers (1-9) that are rounded, and 5 is directly in the middle of them. It could be rounded either up or down, but convention states it should be rounded up, so we do. However, consistently rounding 5 up introduces systematic error: an error that is always wrong in a particular direction.
Let’s look at an example. Consider the numbers 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, and 9.5. The average of these numbers is 5. If we were to round all of these numbers as taught, you get 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. The average of these is 55/10=5.5, which is 0.5 higher than the real average. This means we have an error of 0.5 through this rounding method. A better rounding method for numbers with 5 as their last digit would be to round to the nearest even digit. This gets rid of systematic error as you would be rounding up and down equally often (at least in theory). We can see this clearer through an example. Using the same dataset as above, if we round each number to the nearest even digit, we get 0, 2, 2, 4, 4, 6, 6, 8, 8, 10. The average of this is 50/10=5, meaning we have an error of 0. Although this method of rounding 5s to the nearest even digit helps reduce error (it is actually used quite often in scientific data collection, despite it not being widely known in other contexts), it’s a bit difficult to explain to 7-year-olds. The simplification of always rounding 5 up works well enough for basic applications, but it’s important to keep in mind that it does produce a systematic error. Next time you’re taking data in a science class, try both methods of rounding, and see how much difference there is between the two! Let us know what you find in the comments section.
3 Comments
I agree with most of the article, but I actually disagree with the first paragraph! Your central point seems to be that rounding numbers ending with 5 up is arbitrary convention, but I argue that it is a natural idea, stemming from the 10 digits. Intuitively, because 0-4 are the bottom 5 digits, and 5-9 are the top ten digits, 5 gets rounded up.
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Colton
8/2/2023 06:30:02 am
Well put. To add to that, I'm sure calculus/limits is the more specific field that proves why 0.4999999 rounds down, but 0.5 rounds up. But that kind of abstract thinking can't be taught to elementary students yet because they aren't ready for that. Instead people just need to understand the fact that 0.5 rounds up. I had to fight with a manager at a pizza place that I worked at, trying to steal $1 of my tips by getting this 0.50 rounding thing all wrong. So there are plenty of people that will never be able to grasp why things are the way they are. At least with math, everything can be proven.
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Stevek
2/12/2022 08:24:33 am
If the device used to measure mechanically truncates then rounded up the 5 might make sense.
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