Looking for Errors

This is a secret used by the engineering community. After all, accuracy is vital to good engineering. Thus all engineers check and double check their calculations. In these days of calculators, it is especially necessary to check answers. It is all to easy to press the wrong key. We all know how easy it is to enter one digit wrong when part of a large number. Consider also how often one accidentally one presses the multiply key when you mean to divide or add.

In order to check your work, round off all numbers to one digit and repeat the calculation. When working with single digit numbers, some of us can do the calculation in our heads. Most people can, do the calculation with pencil and paper, but even if one is using a calculator, working with single digits reduces the chance of error.

Of course, working with single digits minimizes the accuracy of the result, but it minimizes the mathematical errors. Your single digit calculation answer should be very close to your original answer. If not, look for errors.

Because you are working with single digits, your single digit calculation is probably correct. It should also be easy to check by inspection, and errors should be very easy to find.

Thus if the two answers are not about the same, spend a lot of time looking for mistakes in your original calculation.

This does not work all the time, but major errors become obvious. If one multiplies in stead of dividing, the difference in answers will be spectacular. If you multiply by 124 rather than 1.24, your answer will be too large by 100. As a rule of thumb, any answer that differs from the single digit calculation by more than ten per cent is probably in error.

I have retired from engineering and now teach Algebra. Another reason I encourage my students to use this method of checking their calculations is that it makes them more confident in their calculations. Many of today’s students are shy about even attempting to do calculations with pencil and paper. Single digit calculations, of course, are easier. There are fewer changes for error. Thus students perform calculations correctly and begin to recognize which answers look right and which look wrong.

By rounding all the numbers to a single digit when you check your work, you can eliminate many of your mistakes. Perhaps you will get an A on your next quiz or get a raise from your boss. In any event, remember that this technique is a secret. Don’t tell anyone else. My fellow engineers will have my head.