Appendix I
ESTIMATING
Often, it makes far more sense to estimate than it does to give an exact answer. Some answers can’t be
given with absolute accuracy; the value of pi is always approximate, as is the value of the square root of
- Both of these values are used and calculated regularly. Even percentage discounts in your department
store are rounded off to the nearest cent or nearest 5 cents. When you are buying paint or other materials
from a hardware store you have to estimate. It is a good idea to estimate high to be sure you have
enough nails, ribbon, or whatever it is you are buying. An exact amount is sometimes not a good idea.
We used the idea of estimation when we looked at standard long division. We rounded off the divisor
to estimate each digit of the answer, then we tested each estimate.
If I am buying computer screens for a school, how much will 58 computer screens cost me if they are
$399 each? To get a rough estimate, instead of multiplying 399 by 58, I would multiply 400 by 60. So,
my estimation is 400 × 60, or 4 × 6 × 100 × 10, which is 24,000. Because I rounded both amounts
upwards I would say 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. The actual amount is $23,142, but my instant estimation tells me
what sort of price to expect.
If I am driving at 100 kilometres per hour, how long will it take me to drive 450 kilometres? Most
students would say 4½ hours, but there are other factors to consider. Will I need fuel on the way? Will
there be hold-ups on the freeway? 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.
The general rule for rounding off to estimate an answer is to try to round off upwards and downwards
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 first
number to 125, or even 100. Then: 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 yard 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 downwards and the other upwards I would expect my answer to be fairly close.
700 × 500 = 350,000
489 × 706 = 345,234
The answer has an error of 1.36%. That 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? That is the major test for any mathematical problem.