secrets-of-mental-math-malestrom

Good Enough: The Art of “Guesstimation” 115
Instead of a 1-by-1 multiplication problem, you now have a
2-by-1 problem, which should be easy enough for you to do.
Your guesstimation is off by only 1.5%.
When you guesstimate the answer to multiplication problems
by rounding the larger number up and the smaller number
down, your guesstimate will be a little low. If you round the
larger number down and the smaller number up so that the
numbers are closer together, your guesstimate will be a little
high. The larger the amount by which you round up or down,
the greater your guesstimate will be off from the exact answer.
For example:
73
65
4745
ª
70
68
4760
Since the numbers are closer together after you round them
off, your guesstimate is a little high.
67
67
4489
ª
70
64
4480
Since the numbers are farther apart, the estimated answer is
too low, though again, not by much. You can see that this multiplication
guesstimation method works quite well. Also notice that
this problem is just 67 2 and that our approximation is just the first
step of the squaring techniques. Let’s look at one more example:
83
52
4316
ª
85
50
4250