EXACT NUMBERS

Certain types of numbers are considered “exact.” For example, there are exactly 16 ounces in one pound. The number 16 would have as many significant figures as needed. So one pound has 16.000000000000.... ounces. Calculations involving this number should not be limited by the significant figures shown in “16 oz/lb.” For example, if we want to calculate how many ounces are in 2.0 lb, we would set up the problem thus:

The answer has 3 sig. fig. even though 16 appears as 2 sig. fig.. The answer is limited by 2.00 lb (3 sig. fig.) and not by 16 because it is an “exact” number. In the same way, the answer is not limited by “1” in “1 lb” because that, too, is an exact number.

Which types of numbers are considered “exact?” Below are the general rules.

1. Conversions between units within the English System are exact.

e.g. 12 in = 1 ft or 12 in/1 ft (In this conversion, 12 and 1 are both exact.)

2. Conversions between units within the Metric System are exact.

e.g. 1 m = 100 cm or 1 m/100 cm (In this conversion, 1 and 100 are both exact.)

3. Conversions between English and Metric system are generally NOT exact. Exceptions will be pointed out to you.

e.g. 1 in = 2.54 cm exactly (1 and 2.54 are both exact.)

e.g. 454 g = 1 lb or 454 g/1 lb (454 has 3 sig. fig., but 1 is exact.)

4. “Per” means out of exactly one.

e.g. 45 miles per hour means 45 mi = 1 hr or 45 mi/1 hr. (45 has 2 sig. fig. but 1 is exactly one.)

5. “Percent” means out of exactly one hundred.

e.g. 25.9% means 25.9 out of exactly 100 or 25.9/100 (25.9 has 3 sig. fig., but 100 is exact.)

6. Counting numbers are exact. Sometimes it is hard to decide whether a number is a “counting number” or not. In most cases it would be obvious. Ask when in doubt.

e.g. There are 5 students in the room. (5 would be an exact number because you cannot have a fraction of a student in the room.)

Practise with Silberberg 4^th Ed, p.36 #68, 69, 72.