This topic review is short and straightforward. In fact, it probably doesn’t deserve to be dedicated its own post. For the past couple of posts I have been discussing significant figures and how to apply them to calculations done in the quantitative science of chemistry. The next thing you need to know about is exact numbers.
Exact numbers are exactly what they sound like. Exact numbers are numbers that do not contain any uncertainty, unlike much of what I discussed in earlier posts. What constitutes an exact number? For one, an exact number is any number that is either (1) counted or (2) defined (Zumdahl and DeCoste 2008). These two terms, counted and defined, are surely a little vague.
When you count something, such as 10 apples on the kitchen counter, 6 towels in the closet, or 2 cars in the driveway, there is no uncertainty to these numbers, despite the fact that they may be performed by you, and you are capable of making an experimental error. It is obvious why there is no uncertainty here: you are not measuring the approximate length of your dog’s tail in centimeters; you are measuring quantities that are clearly visible and which can only be counted as whole numbers, or integers.
The second type of exact number is a number that is defined. All of the conversions you know of between any two measurements (such as miles to kilometers, inches to centimeters, and pounds to kilograms) contain defined numbers that are to be treated as exact numbers when solving problems in chemistry. For instance, one inch is equal to 2.54 centimeters. When performing calculations, you would not apply the rules of the use of significant figures in calculations for either multiplication and division or addition and subtraction to either of these values (whichever is used in the calculation). This value has been predefined and for the purpose of solving the problem, there is to be no uncertainty in this measurement.
So, for both quantities that are counted and quantities that are defined, the rules of significant figures in calculations do not apply, because these types of quantities are assumed to not hold any uncertainty. Thus, these types of quantities will not have any effect on the final answer to your calculation; they can effectively be ignored when determining how many significant figures to provide your final answer with.
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