The Grammarphobia Blog

# Fuzzy numbers

Q: I’ve learned a lot about English from listening to you on the radio, but I take exception to your criticism of teaching approximations in arithmetic. I worked as an engineer for more than 40 years, and I found approximations invaluable. Punching errors are common when using a calculator, so approximating the answer helps protect against doing exact calculations with the wrong data. Approximating requires a solid knowledge of arithmetic, and practicing it enhances that knowledge. I hope you reconsider your stand on this issue.

A: I agree that it’s extremely valuable to know how to make calculations based on approximations. For instance, mathematical errors are apologized for almost every day in the Corrections column of the New York Times, errors that could have been avoided if someone had stopped to make simple approximations.

A recent article in the Times, for example, referred to 100,000 gallons of heating oil instead of 100 million gallons. And another article referred to 2.5 billion in investment funds instead of 2.5 trillion. I could go on, but I’m sure that as a person interested in “numeracy,” you see this stuff too.

Obviously, I’m not opposed to the kind of approximating that you’re talking about. But if this is what kids are being taught in the public schools, it isn’t getting through to them. I see little evidence that these students are achieving anywhere near the level of skill you describe.

For instance, this kind of thing happens to me all the time, and I’m sure it must happen to you, too, especially during the summer-job season: I purchase articles totaling \$19.15 and hand the college-bound cashier a twenty and a quarter; he or she stares at the money in utter paralysis. At last I have to explain, “Give me back one dollar and a dime.”

It seems to me that in order to make the kinds of calculations you’re talking about, one has to begin with a rudimentary knowledge of addition, subtraction, multiplication, and division. But the multiplication tables are no longer part of the curriculum in many school districts. And neither is English grammar.

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