"Convenience" is the Main Reason Why We Round Off Numbers

© 2010 Ugur Akinci
We technical communicators deal with numbers all day long. We write them, calculate them, interpret them. We also round them off.
“What’s the best way to round off numbers?” a reader asked. And I did some thinking about it because I realized I haven’t given it enough thought in the past. That was a surprising discovery, frankly. Here are some of my results…
When we round off a number we lose information, no doubt. When 3.89 becomes 3.9 or 4 not 4.0. 4.0 is just a wrong version of 3.9, it is not rounding. , there is some fudging there to be sure. There is an “exaggeration” there. We make the number larger than it really is.
Reverse is equally troublesome. When we round 14.12 down to 14.1 or to 14, we chuck away something. We make the number smaller than it really is.
The issue here is one of significance; whether, in the larger scheme of things, the part that we lost or the part that we created makes sense or not.
For example, imagine we are measuring the distance between the galaxies. Does it make sense to report it in millimeters? I don’t think so because that type of distance is reported in light years, or in millions of miles. A millimeter is such a small part of a light year that it is practically unmeasurable. Thus the unit of measurement has a lot to do whether a rounding off makes sense or not.
If the unit of measurement is in light years, to round off 3.69 light years to 3.7 light years is significant. It makes sense. But to round off 3.5700089 x E-10 millimeters to 3.570009 x E-10 millimeters probably does not make much sense. At least, it would be difficult for a lot of people to understand the significance of it right away. It would not be a “user friendly” rounding off.
Another example: if you measured the length of your computer screen by using a ruler with millimeters on it, the fraction of the millimeter in your measurement is not accurate (not significant). So if you say that “my screen is 40.67 cm,” you should round it to 40.7 cm because you are not able to measure the fraction (the second digit after the decimal point) of a millimeter. But if you are measuring it with a ruler that shows the fraction of millimeter, then 40.67 is accurate and should not be rounded off.
So the unit of measurement must be appropriate for the objects in question for any rounding off to make sense; or at least to make sense “easily”.
We round off numbers because it’s easier to understand and remember shorter numbers. We do it because it’s the convenient thing to do.