Numbers Exact and Counted Versus Measured

If I ask you to count the number of automobiles that you and your family own, you can do it without any guesswork involved. Your answer might be 0, 1,2, or 10, but you would know exactly how many autos you have. Those are what are called counted numbers. If I ask you how many inches there are in a foot, your answer will be 12. That is an exact number. Another exact number is the number of centimeters per inch — 2.54. This number is exact by definition. In both exact and counted numbers, there is no doubt what the answer is. When you work with these typ of numbers, you don t have to worry about significant figures. 

Now suppose that I ask you and four friends to individually measure the length of an object as accurately as you possibly can with a meter stick. You then report the results of your measurements 2.67 meters, 2.65 meters, 2.68 meters, 2.61 meters, and 2.63 meters. Which of you is right You are all within ocperimental error. These measurements are measured numbers, and measured values always have some error associated with them. You determine the number of significant figures in your answer by your least reliable measured number. 

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