Section 2-3 Section 2.3 Uncertainty in Data Define and compare accuracy and precision. experiment: a set of controlled observations that test a hypothesis Describe the accuracy of experimental data using error and percent error. Apply rules for significant figures to express uncertainty in measured and calculated values.

Section 2-3 Section 2.3 Uncertainty in Data (cont.) accuracy precision error Measurements contain uncertainties that affect how a result is presented. percent error significant figures

Section 2-3 Accuracy and Precision Accuracy refers to how close a measured value is to an accepted value.Accuracy Precision refers to how close a series of measurements are to one another.Precision

Example: The acceleration due to gravity on Earth is 9.8 m/s 2. Look at the lab data for two students. Whose data was most accurate? Whose data was most precise? How would you describe Fred’s data? Sue’s Trials Calculated acceleration (m/s 2) Fred’s Trials Calculated acceleration (m/s 2)

Section 2-3 Accuracy and Precision (cont.) Error is defined as the difference between and experimental value and an accepted value.Error The error equation is error = experimental value – accepted value.

Example: The acceleration due to gravity on Earth is 9.81 m/s 2. Look at the lab data for two students. What is the error for Sue’s trial 3? What is the error for Fred’s trial 1? Sue’s Trials Calculated acceleration (m/s 2) Fred’s Trials Calculated acceleration (m/s 2)

Section 2-3 Accuracy and Precision (cont.) Percent error expresses error as a percentage of the accepted value. The percent error is always expressed as an absolute value.Percent error

Example: The acceleration due to gravity on Earth is 9.81 m/s 2. Look at the lab data for two students. What is the % error for Sue’s trial 3? What is the % error for Fred’s trial 1? Sue’s Trials Calculated acceleration (m/s 2) Fred’s Trials Calculated acceleration (m/s 2)

In a lab, students were to calculate the density of aluminum. The accepted value is 2.7 g/cm 3. In George’s experiment, they found the value to be 2.5 g/cm 3. Find: A). George’s error: B). George’s percent error:

A.A B.B C.C D.D Section 2-3 Section 2.3 Assessment A substance has an accepted density of 2.00 g/L. You measured the density as 1.80 g/L. What is the percent error? A.0.20 g/L B.–0.20 g/L C.0.10 g/L D.0.90 g/L

2.3 Significant Figures –(Sig Figs)

Section 2-3 Significant Figures Often, precision is limited by the tools available. Significant figures include all known digits plus one estimated digit.Significant figures

Section 2-3 Significant Figures (cont.) Rules for significant figures –Rule 1: Nonzero numbers are always significant. –How many significant figures in each of the following:

Rule 2: Zeros between nonzero numbers are always significant. (sandwich rule) How many significant figures?

Rule 3: All final zeros to the right of the decimal are significant. (You shouldn’t tack a zero on after the decimal if you don’t actually measure it). How many significant digits?

Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation. In , the 3 zeros are just place-holders…they are just showing that the number is eleven-thousand, not eleven. How many significant figures?

Rule 5: Counting numbers and defined constants have an infinite number of significant figures. What this means….if you say there are 8 people in the room, that has infinite significance. You can’t have 8.2 people…or 7.9 people. If you were to average 3 masses, 55.5 grams, 54.6 grams and 53.5 grams….how would you do that? The 3 that you divide by has infinite significance since it is a counting number.

Section 2-3 Rounding Numbers Calculators are not aware of significant figures. When we find the answers to problems, the significant figures in the answer will be calculated based on the significant figures in the original data. Answers will usually be rounded.

Section 2-3 Rounding Numbers (cont.) Rules for rounding –Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant figure. –Rule 2: If the digit to the right of the last significant figure is greater than 5, round up to the last significant figure. –Rule 3: If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up to the last significant figure.

Section 2-3 Rounding Numbers (cont.) Rules for rounding (cont.) –Rule 4: If the digits to the right of the last significant figure are a 5 followed by a 0 or no other number at all, look at the last significant figure. If it is odd, round it up; if it is even, do not round up. (round to the nearest even number). –There is a reason for this rule. If you don’t do this, you are constantly skewing your lab results to the high end. Let’s look at an example.

Trial # Time (sec) Trial #Time (sec) old rounding Trial #Time (sec) New rounding What is the average? What is the average of the rounded values?

If we consistently round up in a lab setting (like you have probably done your whole life), you are constantly skewing the results upward. By rounding with the even rules, the round “ups” balance the round “downs” and the data is more true to what it should be.

Section 2-3 Rounding Numbers (cont.) Rule for Addition and subtraction with significant figures – Round numbers so the answer is significant to the same column as the least significant number. – Huh???? m m

Let’s look at an example: –Joe, Sally, and Fred count the money in their piggy banks. –Joe counts only the dollars. He says he has $43. in his bank. –Sally counts only the dollars and dimes. She says she has $53.4 in her bank. –Fred counts all the money in his bank. He ends up with $ –If we add their totals together, we get Is this really the total for the three banks?

–If we add their totals together, we get Is this really the total for the three banks? Of course not….because we don’t know how many pennies Sally had…or dimes or pennies that Joe had. The best we can do is to say that the three had a total of about $119.

In the same way, the results in an addition or multiplication can only be good to the least accurate place of any one of the numbers. Examples:

Rule for Multiplication and division with significant figures –Round the answer to the same number of significant figures as the original measurement with the fewest significant figures. –In other words, your answer can’t have more significant figures than the number with the fewest significant figures.

Examples: Multiply or divide the following, maintaining significance x 22.3 = 13.1 x 102 = 22.0 x =

A.A B.B C.C D.D Section 2-3 Section 2.3 Assessment Determine the number of significant figures in the following: 8,200, 723.0, and A.4, 4, and 3 B.4, 3, and 3 C.2, 3, and 1 D.2, 4, and 1

End of Section 2-3

Section 2-4 Section 2.4 Representing Data Create graphics to reveal patterns in data. independent variable: the variable that is changed during an experiment graph Interpret graphs. Graphs visually depict data, making it easier to see patterns and trends.

Section 2-4 Graphing A graph is a visual display of data that makes trends easier to see than in a table.graph

Section 2-4 Graphing (cont.) A circle graph, or pie chart, has wedges that visually represent percentages of a fixed whole.

Section 2-4 Graphing (cont.) Bar graphs are often used to show how a quantity varies across categories.

Section 2-4 Graphing (cont.) On line graphs, independent variables are plotted on the x-axis and dependent variables are plotted on the y-axis.

Section 2-4 Graphing (cont.) If a line through the points is straight, the relationship is linear and can be analyzed further by examining the slope.

Section 2-4 Interpreting Graphs Interpolation is reading and estimating values falling between points on the graph. Extrapolation is estimating values outside the points by extending the line.

Section 2-4 Interpreting Graphs (cont.) This graph shows important ozone measurements and helps the viewer visualize a trend from two different time periods.

A.A B.B C.C D.D Section 2-4 Section 2.4 Assessment ____ variables are plotted on the ____-axis in a line graph. A.independent, x B.independent, y C.dependent, x D.dependent, z

A.A B.B C.C D.D Section 2-4 Section 2.4 Assessment What kind of graph shows how quantities vary across categories? A.pie charts B.line graphs C.Venn diagrams D.bar graphs

A.A B.B C.C D.D Chapter Assessment 1 Which of the following is the SI derived unit of volume? A.gallon B.quart C.m 3 D.kilogram

A.A B.B C.C D.D Chapter Assessment 2 Which prefix means 1/10 th ? A.deci- B.hemi- C.kilo- D.centi-

A.A B.B C.C D.D Chapter Assessment 3 Divide 6.0  10 9 by 1.5  A.4.0  10 6 B.4.5  10 3 C.4.0  10 3 D.4.5  10 6

A.A B.B C.C D.D Chapter Assessment 4 Round the following to 3 significant figures A.2.35 B C.2.34 D.2.40

A.A B.B C.C D.D Chapter Assessment 5 The rise divided by the run on a line graph is the ____. A.x-axis B.slope C.y-axis D.y-intercept

A.A B.B C.C D.D STP 1 Which is NOT an SI base unit? A.meter B.second C.liter D.kelvin

A.A B.B C.C D.D STP 2 Which value is NOT equivalent to the others? A.800 m B.0.8 km C.80 dm D.8.0 x 10 5 cm

A.A B.B C.C D.D STP 3 Find the solution with the correct number of significant figures: 25  0.25 A.6.25 B.6.2 C.6.3 D.6.250

A.A B.B C.C D.D STP 4 How many significant figures are there in meters? A.4 B.5 C.6 D.11

A.A B.B C.C D.D STP 5 Which is NOT a quantitative measurement of a liquid? A.color B.volume C.mass D.density