Significant digits

Significant Digits

When reporting the result of a measurement, you only report the digits you are reasonably sure of. True, the last digit you report will have some uncertainty in it, but it its not completely uncertain; you have estimated it based on your measurement. Each of these reported digits is significant. Suppose you wanted to report the number of people who showed up for your school's football game. Even if tickets were collected for the game, you wouldn't really want to count all of the ticket stubs. Instead, you look around the stadium and notice that it is about 3/4 full. If your stadium seats 6000 people, you would report a crowd of 4500 attending the game.

Now, let's talk sig-digs. You don't really mean to report that exactly 4500 fans were at the game. There could have easily been 4501 fans, 4450 fans, even 4300 fans. But you're pretty sure the number wasn't 3500 or 5500 fans. The zeroes are just place-holders; they are not significant. The 4 and the 5, however, are significant. You're certain about the 4, and the 5 is estimated but approximately correct. This example illustrates the first rule of significant digits:

Any non-zero digit in a reported number is significant.