Math rules

Why and when do we estimate?

Sometimes we don't have (and can't get) exact data to determine an exact answer.

Sometimes we aren't concerned with an exact answer.

Sometimes we don't have the calculating power (or time) available for an exact answer.

Often, you estimate as a double check. You probably do this with your check book. If you write out around $1000 in bills, you expect your balance to drop by around that amount. If your calculator comes up with a different answer, you double check your math. It is easy to make a mistake with a calculator. You should have some idea what the answer is before you start.

I taught estimation in the classroom. One of my favorite problems was to toss out a phone book and ask by looking at the phone book of some small town in Ohio, estimate how many plumbers are there in Cincinnati.

Estimation is a handy tool for just those reasons markr said, and one that engineer would also acknowledge, particularly since engineering is generally a field where three significant digits is exact.

I always had exactly the opposite problem with accountants. I always wondered why they were concerned with pennies out of a million. Later I saw the wisdom, and am willing to understand accountings anal retentiveness, and the necessity of counting pennies on the tail of millions.

Oh, every time you are reading a clock, it is effectively estimation. The reading of the clock face varies according to stance, and if you read it from the far right or left your estimation of time becomes worse.

Rap

I saw an interesting use of approximation the other day. You can estimate the number of words you know by opening a dictionary to a random page and seeing how many words on the page you know. Then multiply by the number of pages in the dictionary. I think the standard deviation would be high, but it sounds like an interesting thing to try.