SOME NOTES ON ARITHMETIC

KEEPING CALCULATIONS ON TRACK

Have two colleagues work the same problem. They should be in different places and they should not communicate at all until they are sure of their solutions. They should also agree on the rough layout of their calculations so that comparisons can be made the more easily.

Write out the units on each line of the calculation.

Even when the units are written out, think about dimensions all the time.

Pay close attention to which units are being used. American gallons are not the same as British gallons and the distance of one mile has a notable number of different meanings.

Convert all units to their SI equivalent and calculate in SI units. If there is no choice, then convert back to indigenous units at the end.

Pay attention to what assumptions are being made. Sometimes it's not worth bothering with a badly described problem.

Decide what accuracy in the answer is needed.

Decide how to deal with rounding errors.

ASSUMPTIONS

The most straight forward of calculations needs to be looked at to see if it makes sense :

If three men mow six fields in two days, how long will it take one man to mow three fields ?

Although we all know that this is just an exercise for school kids at some particular level of tuition, it can serve as a reminder that in the real world arithmetic by itself need not yield even an approximation to reality.

Without thinking very hard, we can easily write down a few assumptions that we'd need to check with a paying customer :

The fields are the same size

The grass is in the same condition in each field

Each man mows at the same rate as the other two individuals

All mowing is done day after day and is not interrupted for Feast Days, the weather or for any other reason

A single man works at the same rate as he would work when working in the team

The three men were working separately. You could imagine that the three men were working on a three-man mowing machine. In this case, a single man would have to revert to another type of mower or a scythe and the calculation can't go ahead.