Wednesday, June 2, 2010

What are Significant Figures?

Significant Figures are a concept that is introduced to students usually in Introductory Science courses, right near the beginning. However, it is a concept that continually confuses people, even beyond their school years. This is because, at first glance, Significant Figures appears to be the same as rounding... but there are many rules to follow, and that is where most of the difficulty arises.

As I said, the concept of Significant Figures ("sig figs") is associated with rounding, but there is more to it. It also describes the amount of uncertainty there is in a value, and is tied to that value's accuracy and precision. They are the digits in a value that are considered to be important, as a result of the precision in their measurement.

Here are a few basic examples:
  • A thermometer reads 26.9 degrees Celsius. This is 3 sig figs.
  • A scale displays a weight of 31.22 g. This is 4 sig figs.
  • A stopwatch shows 58.778 seconds. This is 5 sig figs.
So far, so good, right? Now, let's throw in a wrinkle. Sometimes, you don't count a zero as a Significant Figure. You ignore them ONLY IF they are at the very start of a number, such as before a decimal place, or at the very end of a number, such as 10.

Here are some more examples:
  • The number 0.232 has 3 significant figures.
  • The number 0.0076 has 2 significant figures.
  • The number 0.000000000000003 has 1 significant figure.
  • The number 100 has 1 significant figure.
  • The number 82000 has 2 significant figures.
  • The number 3,758,200,000,000,000 has 5 significant figures.
So, with those examples, you can hopefully now see how many significant figures a number with just a quick look.

Read on, where I will outline the general rules for determining the number of sig fig's, and also rules on how to do math with them.

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