© 2010 Ugur Akinci
Is there a limit to rounding off numbers? Yes there is.
The digits after the decimal point reflects the degree of uncertainty we have inherent in the measurement (and thus in the number) itself. For example, 10.7 is less exact, less accurate, than 10.743. Thus we can say that we are “more sure” about 10.743; that 10.743 is “more accurate” than 10.7. Another way of expressing the same thing would be to say that, comparatively, 10.7 is “less accurate” than 10.743.
One complication thrown our way is the merciless divisions made by all calculators today. Try dividing 15 into 7 and see what happens… If I had to answer that question from the top of my head, I’d report the result of the division as “something a little more than two, 2.2 or something.” But a calculator’s answer would be 2.1428571.
Now how are going to round off this answer? Should it be 2.142857? Or 2.1? Or perhaps something in between?
Again, we have to think about the context and decide whether it “makes sense” or not. “2.1 percent interest rate” makes perfect sense. But “2.142857 slices of apple” does not.
Secondly, I’d look at the numerator (the number at the top) and the denominator (the number at the bottom) of a division. Since we cannot create “something” out of “nothing,” similarly, we cannot create a “more accurate” number out of the division of two “less accurate” numbers. It just does not make sense. The calculators would generate such a number easily of course, as in the case of dividing 15 into 7. But the “more accurate” result would not be significant.
That brings us to my second rule in rounding off numbers: limit the total number of digits-after-the-decimal-point of your answer to the smaller of the total number of digits-after-the-decimal-point in the numerator and denominator. Do your rounding off accordingly.
For example, let’s say you are dividing 20.235 (3 digits-after-the-decimal-point) into 4.7 (1 digit-after-the-decimal-point). The calculator answer is 4.3053191. I would round this result off such that the answer would also have only 1 digit-after-the-decimal-point. Thus my answer would be 4.3.
For example: 20.235 / 1.2 = 16.8625 should be rounded to 16.9, not 17 or 16.863.
Another important point: A number with ZERO after the decimal point is NOT the same thing as the same number with NO decimal point! Did you know that?
For example, 4 is not the same thing as 4.0.
“4.0” means you know the number up to the first digit after the decimal point.
“4”, on the other hand, means you don’t know the number up to the first digit after the decimal point; what you know for sure is/are only the units digit(s).
Even such a seemingly simple thing as rounding off numbers has such mysteries hidden in it, doesn’t it?