1. Significant Figures (HOW TO KNOW WHICH DIGITS OF A NUMBER ARE IMPORTANT)

2. How Accurately Can You Measure with This?  Could you find measurements like this?  1 inch  2.5 inches  3.1 inches  4.6348 inches

3. Accuracy  We want our numbers to convey the level of accuracy we had when measuring  Math operations can lead to problems with this:  1.0/3.0 = 0.33333333333333333333333  (The answer looks a lot more precise than the numbers we started with)  So, we keep track of the number of significant digits we start with, and use it to round our answer.  1.0/3.0 = 0.33

4. Rules for Significant Digits  Count the number of digits:  45.1 = 3 sig figs  612 = 3 sig figs  9.12345 = 6 sig figs  Zeroes are tricky: .0000005 NOT significant  6300 NOT Significant  6300. Significant  705 Significant  (Try putting the number in scientific notation, if the zeroes go away, they’re not significant)

5. Practice with Zeroes  How many significant figures do each of these numbers have?  5437.2  890  650.0  85  80 .0098  6.004  0.008  602  More Practice:  5,067  4,080  9.01 .01 .00302  10.004  6.120

6. Math With Significant Figures  Adding / Subtracting  Look at all the numbers you started with.  Find the one with the least number of digits after the decimal place.  Round your answer to that number of decimal places.  Multiplying / Dividing  Look at the numbers you started with.  Find the one with the least number of significant digits.  Round your answer to that number of significant digits

7. Adding/Subtracting  Example:  42.0 +.13 = 42.13  42.0 has one digit after the decimal,.13 has two, so I’ll round the answer to 1 digit after the decimal.  Answer: 42.1  That means this is true:  5 +.4 = 5  Why?

8. Keep in mind that ‘5’ doesn’t mean 5 anymore  When we write ‘5’ now, what we really mean is that our number is somewhere between 4.5 and 5.4.

9. Adding and Subtracting Practice  4.12 +.1 =  520 +.02 =  12 + 5.1 =  36.8 – 4 =  5.34 -.2 =

10. Multiplying and Dividing  Example:  5.2 x 7 = 36.4  5.2 has 2 sig figs, 7 has 1, so we’ll round it to 1 sig fig  5.2 x 7 = 40  Practice: .03 x 5.21  6.2 x 10  5.780 x 2.0617  6 x.1  92 /.03  12 / 4.01