 Importance: to ensure the accuracy of our measurements  To make sure we tell others only what we actually know based on our equipment and it’s limitations  Accuracy- measure of how close a measurement comes to the actual or true value  Precision- measure of how close a series of measurements are to one another

 Error: experimental value – accepted value  Percent error: absolute value of the error divided by the accepted value, multiplied by 100% Our goal this year is less than 5% error in experiments!

 Significant figures: all the numbers actually measured plus one that is estimated

 Non zeros are always significant:  has 6 sig figs  Zeros within a number are always significant. Both 4308 and contain four significant figures.  Zeros that do nothing but set the decimal point are not significant.  470,000 has 2 significant figures has 2 sig figs  Trailing zeros that aren't needed to hold the decimal point are significant.  4.00 has 3 significant figures.  has 2 significant figures  Exact counts and definitions have infinite significant figures- like 12 people. There is no estimation.

 look for the presence of a decimal point  this will tell you which side to start counting from  Pacific: decimal Present ▪ Start counting from the left at the first nonzero number ▪ Would have 4 sig figs  Atlantic: decimal Absent ▪ Start counting from the right at the first nonzero number ▪ would have 3 sig figs

a)314.7 meters x 10 2 meters b) meters1.8 x meters c)8800 meters8.8 x 10 3 meters

 The number of decimal places in the answer is equal to the number of decimal places in the quantity with the smallest number of decimal places  =

 The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer.  2 x 10.0 = 20  66 / 2 = 33 = 30  x 2.0 = 10.01= 10. or 1.0 x 10 1

 When you add two numbers, you add their uncertainties, more or less. If one of the numbers is smaller than the uncertainty of the other, it doesn't make much of a difference to the value (and hence, uncertainty) of the final result. Thus it is the location of the digits, not the amount of digits that is important.  When you multiply two numbers, you more or less multiply the uncertainties. Thus it is the percentage by which you are uncertain that is important -- the uncertainty in the number divided by the number itself. This is given roughly by the number of digits, regardless of their placement in terms of powers of ten. Hence the number of digits is what is important.

 Round all of these numbers to 3 significant figures      

 1. In which of the following expressions is the number on the left NOT equal to the number on the right? ▪  10 –8 = 4.56  10 –11 ▪ 454  10 –8 = 4.54  10 –6 ▪  10 4 =  10 6 ▪  10 6 = 4.52  10 9

 2. Which set of measurements of a 2.00-g standard is the most precise? ▪ 2.00 g, 2.01 g, 1.98 g ▪ 2.10 g, 2.00 g, 2.20 g ▪ 2.02 g, 2.03 g, 2.04 g ▪ 1.50 g, 2.00 g, 2.50 g

 3. A student reports the volume of a liquid as L. How many significant figures are in this measurement? ▪ 2 ▪ 3 ▪ 4 ▪ 5