Why are measurement units important? Why do we use significant digits? What do you think? Why are measurement units important? Why do we use significant digits? Why use scientific notation? 1

What do you think? Why are measurement units important? - For communication and standards Why do we use significant digits? - To specify the precision in a measurement Why use scientific notation? - To more conveniently express very large or very small numbers. 2

Unit Conversion Prefixes are used to change SI units by powers of 10, as shown in the table below. 3

Unit Conversion A method of treating units as algebraic quantities, which cancel (or divide out), is called unit conversion or dimensional analysis. For example, to convert 1.34 kg of iron ore to grams, do as shown below: 4

How long is the pencil? 5

Significant Digits Significant digits (or figures) are needed when performing calculations with measurements. We need a set of guidelines when we do calculations so that we get rid of all those 4.243956528452940472 answers you see on your calculator. The guidelines tell us how many digits we should round off the final answer to show the correct precision or SIGNIFICANT DIGITS. To determine the number of SIGNIFICANT (or important) DIGITS follow several rules. 6

Significant Digits 1) The numbers 1 to 9 are always significant digits. 0 is a significant digit if it comes between of a number between 1 and 9. Example: 13.869  five significant digits 1.304  four significant digits. The zero counts because it appears between the “3” and “4” 7

0.08  one significant digit. Significant Digits 576.00  five significant digits. The zeros count because they appear to the right of the “6” and after the decimal. 0.08  one significant digit. The zeros don’t count, because they are to the left of the “8”. 8

Significant 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: 11.623 2.0 + 0.14 13.763  round it off to 13.8, since the number “2.0” is the least precise… it only has one significant digit after the decimal. 9

Significant Digits 3) When you multiply or divide numbers, check which number has the fewest significant digits. Round off your answer so it has that many significant digits. Ex: 4.56 x 13.8973 = 63.371688  63.4 We round off our final answer to three significant digits, because “4.56” has the fewest significant digits… three. 10

What do you think? Why do we make graphs? What do graphs tell us that makes their use important to data analysis? 11

Graphing Data Graph the relationship between independent and dependent variables. Interpret graphs. Recognize common relationships in graphs. 12

Graphing Data Identifying Variables A variable is any factor that might affect the behavior of an experimental setup. The independent variable is the factor that is changed or manipulated during the experiment. The dependent variable is the factor that depends on the independent variable. 13

Graphing Data 14

Graphing Data Linear Relationships When the line of best fit is a straight line, as in the figure, the dependent variable varies linearly with the independent variable. This relationship between the two variables is called a linear relationship. The relationship can be written as an equation. 15

Graphing Data Linear Relationships The y-intercept, b, is the point at which the line crosses the y- axis, and it is the y-value when the value of x is zero. 16

Graphing Data Nonlinear Relationships When the graph is not a straight line, it means that the relationship between the dependent variable and the independent variable is not linear. There are many types of nonlinear relationships in science. Two of the most common are: the quadratic and inverse relationships. 17

Nonlinear Relationships Quadratic Relationships A quadratic relationship exists when one variable depends on the square of another. A quadratic relationship can be represented by the following equation: 18

Nonlinear Relationships Inverse Relationships In an inverse relationship, a hyperbola results when one variable depends on the inverse of the other. An inverse relationship can be represented by the following equation: 19

Interpreting Graphs Making Predictions The relationship between variables, either represented as formulas or graphs, can be used to predict values you have not measured directly. Scientists use models, including formulas and graphs to accurately predict how objects will behave when variables affecting their behavior change. 20

When is measurement data precise? When is measurement data accurate? What do you think? When is measurement data precise? When is measurement data accurate? 21

Precise - data points are all very close to each other. Precision & Accuracy Precise - data points are all very close to each other. Accurate - data points all agree with the true value. 22

Precision & Accuracy Example: You perform an experiment to measure the temperature at which water boils. You set up three containers of water and heat each one. At the instant the water boils you measure the temperature and get the following results: 67°C, 68°C, 68°C, 65°C, 66°C Notice these values are precise (they are almost the same, they agree with each other), but they are not accurate. They should be at about 100°C, the accepted value. 23

Precision & Accuracy Example: You give someone a meter stick and ask them “How tall is the doorway?” They come back to you and tell you it is 1.876534693 meters high. Is it possible for them to make a measurement like this with a meter stick? Nope! That’s too many decimal places! To be that accurate you would need a laser. 24

Precision & Accuracy Remember: As a rule of thumb, look at the smallest unit on your measuring device. You can probably measure to within that… Most rulers show millimeters. You could safely measure something with a regular ruler to within a millimeter. 25

Precision & Accuracy In the door example, it would be more reasonable for the measurement to be 187.7 cm (notice that I give the value to within a millimeter). And always remember to choose the right units! Don’t measure a person’s height in kilometers. 26