ffirs.indd

226 Appendix I
I actually have to pay a bit less than $24,000. Of course, when it
comes time to pay, I want to pay exactly what I owe. Th e actual
amount is $23,142, but my instant estimate tells me what sort of
price to expect.
If I am driving at 60 miles per hour, how long will it take me to
drive 300 miles? Most students would say 5 hours, but there are
other factors to consider. Will I need gas on the way? Will there be
traffi c jams? Will I want to stop for a break or have a meal or snack
on the way? My estimate might be 6 hours. Also, past experience
will be a factor in my estimation.
Th e general rule for rounding off to estimate an answer is to try to
round off upward and downward as equally as you can.
How would you round off the following numbers: 123; 409; 12,857;
948; 830?
Your answers would depend on the degree of accuracy you want.
Probably I would round off the fi rst number to 125, or even 100.
Th en: 400; 13,000; 950 or 1,000; and 800 or 850. If I am rounding
off in the supermarket and I want to know if I have enough cash in
my pocket, I would round off to the nearest 50 cents for each item.
If I were buying cars for a car lot, I would probably round off to the
nearest hundred dollars.
How would you estimate the answer to 489 × 706? I would multiply
500 by 700. Because one number is rounded off downward and the
other upward, I would expect my answer to be fairly close.
700 × 500 = 350,000
489 × 706 = 345,234
Th e answer has an error of 1.36%. Th at is pretty close for an instant
estimate.
Estimating answers is a good exercise, as it gives you a feel for the
right answer. One good test for any answer in mathematics is, does it
make sense? Th at is the major test for any mathematical problem.
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