Scientists take the ideas of precision and accuracy very seriously.

• You can actually take entire courses in University that show how to figure out the precision and accuracy of measurements.
  • Guess what? I took 'em!... your opinion of me has probably slipped a few notches ; )
• We need to know that when another scientist reports a finding to us, we can trust the accuracy and precision of all the measurements that have been done.
• A set of guidelines is needed while we do calculations so that we get rid of all those "4.243956528452940472" kind of answers you see on your calculator.
• The guidelines are there so we will know how many digits we should round off the final answer to show the correct precision.

All of this boils down to something called "Significant Digits", more commonly referred to as Sig Digs.

To determine how many significant (important) digits a number has, follow these rules:

1. The numbers 1 to 9 are always sig digs. Zero ("0") is a sig dig if it comes to the right of a number between 1 and 9.

Example 1:

• 13.869 -> Five sig digs. All the numbers are digits between 1 and 9.
• 1.304 -> Four sig digs. The zero counts because it appears to the right of the "3"
• 576.00 -> Five sig digs. The zeros count because they appear to the right of the "6"
• 0.0008 -> One sig dig. The zeros don’t count, because they are to the left of the non-zero digits.

2. When you add or subtract numbers, always check which of the numbers is the least precise (least numbers after the decimal). Use that many decimals in your final answer.

Example 2:

11.623 + 2.0 + 0.14 = ?

If you type this on a calculator, you'll get 13.763. Round it off to a final answer of 13.8, since the number "2.0" is the least precise... it only has one sig dig after the decimal.

We do this because we can’t really trust how much rounding off might have been done for any decimals after this.

3. When you multiply or divide numbers, check which number has the fewest sig digs. Round off your answer so it has that many sig digs.

Example 3:

4.56 x 13.8973 = 63.371688 = 63.4

We round off our final answer to three sig digs, because "4.56" has the fewest sig digs... three sig digs.

Your Data Sheet...

You'll see that there are a bunch of constants on the back of your data sheet. These are all given as three sig digs, so treat them appropriately.

You'll also notice that some formulas already have numbers on them. These numbers are considered perfect and can be considered to have an infinite number of sig digs.

There are also situations where you might need to convert a number from one set of units to another. For example, 1 minute = 60 seconds. This doesn't mean that 1 minute kind of equals 60 seconds... it is a perfect conversion, and does not count for sig digs!