(C) - Copyright, 1996 F.W. Boyle, Jr.

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Some examples of this are:

1) An estimate of the number of jelly beans in a jar is 3250. An average jelly bean weight is found to be 1.2977 g. How much do the jelly beans weigh?

In order to understand significant figures, we must look at each value separately.

First the number 3250 really only has 3 digits in it. The
trailing zero (0) is called a place holder and is not accurate
**UNLESS** the number is stated to be 3250.0. In this latter
form the number is said to be exact. For this problem the number
was not exact but was estimated to be 3250. In scientific
notation, 3250 is written as 3.25x10^{3}. Thus when
written in scientific notation it is easier to determine the
number of actual digits in a number.

The second number, 1.2977, has 5 digits and is already in scientific notation.

Since 3.25x10^{3} has only 3 digits the maximum number of
digits acceptable for calculating the weight of all the jelly
beans is 3 digits.
To do the math we use ALL the digits thus:

3.25 X 10But our answer can only have 3 significant figures since the least number of significant figures in the numbers being multiplied is 3. So the next step is to look at the digit just to the right of the last significant figure. In this case the last significant figure is 1 and the number to the right of it is 7. So the number one will be rounded up to 2 and all the other digits will be dropped. The answer is then:^{3}x 1.2977 -------- 4.21752 x 10^{3}

Now for some practice in counting significant figures.

Try these numbers on your own:

1) 1.000004 2) 9240000 3) 0.000000000011 4) 0.010001 5) 109267 6) 3.2 x 10^{5}