Question

Dear Mitch,

Do you have any quick tip for those SAT questions that give you the feeling you have to plug a million numbers into your calculator, like when there's a million decimal places, even when they ask for only the best approximate answer?

Sincerely,

Dave V. And Barbara W.

Answer

Dear Dave V. and Barbara W.,

On the multiple choice math part of standardized tests, such as the SAT, very often rounding the numbers they give you to work with and checking your work by practiced estimation to see if it seems right is a lot more likely to lead you to the correct choice than working away with your calculator.  (And working with your rounded numbers usually turns out to be much faster than even punching in numbers to your calculator at all!)

Look at the following example:

The best approximate answer for 1.2506311 x 72.9737343 is:

A) 10.5

B) 71.3

C) 79.2

D) 90.5

E) 10.9 

Round the 1.25 ... into just 1 1/4.

Round the 72.97... into just 73.

Now, what is 1 1/4   x   73?

Well, 1 x 73 is 73, and 1/4 of 72 (which is very close to 73 but divides nicely into fourths), is...

Well, a fourth of something is half of a half of it.  So half of 72 is 36, and half of 36 is 18.

So now you add the 73 and the 18 and you get 91. (And this is especially likely to be close since we rounded one of the factors they gave us up a little and the other factor down a little, which tends to balance things out a bit closer to the exact answer!)

Choice D, 90.5 is certainly the closest choice to 91. And, indeed, that is the correct answer!

Hope this helps,

Mitch