Group A Group B Group C 1) crucible g g g 2) evaporating dish g g g 3) mortar g g 177.

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1 Chapter 2 Measurement and Calculations Measuring the Book L = W = H = What is the volume of the book? What is the area of the cover of the book? **If the book has a mass of 2.5 kg, what is its density? Measuring Volume and Uncertainty Group A Group B Group C Group D 1) 180 ml 260 ml 190 ml 100 ml 2) ) ) ) Measuring Mass and Uncertainty Group A Group B Group C 1) crucible g g g 2) evaporating dish g g g 3) mortar g g g Sep 25 8:05 AM 1

2 Accuracy and Precision What is accuracy? What is precision? Describe each. Accuracy and Data Error or Percent Error Precision and Data Deviation Data Tables (please reproduce on a separate sheet of paper!) Procedure l: Title??? (Be Descriptive...What is this data?) Trial Measured Length (cm) % Error [5.00 measure]/ 5.00 x 100 Deviation [measure mean] Average Average Sample Calculations: 1) Average: 2) % Error: 3) Deviation: Procedure 2: Title! (Be Descriptive) Average Trial Dollar Bill Drop (cm) Meterstick Drop (cm) Group Average (you and 4 others) Deviation [your average group average] Procedure 3: Title! (Be Descriptive) Trial Measured Time (s) % Error [20.00 s Measure]/ X Average *Average Deviation [average of each deviation from average] *Deviation = [measured time average] Trial 1 = Trial 2 = Trial 3 = Trial 4 = Average Deviation = Sep 25 1:10 PM 2

3 Class Average for Drops of Water on Penny Name Average # of Drops Class Average Sep 30 1:05 PM 3

4 Class Average for Drops of Water on Penny Name Ave # of Drops Class Average Oct 1 8:09 AM 4

5 Class Average for Drops of Water on Penny Name Average # of Drops Class Average Oct 1 11:54 AM 5

6 Scientific Method Identify the Problem Form a Hypothesis Create and Perform an Experiment Analyze the Data Modify the Experiment Communicate the Results Sep 25 2:04 PM 6

7 Scientific Variables Independent variable The independent variable is the one condition that you change in an experiment. Example: In an experiment measuring the effect of temperature on solubility, the independent variable is temperature. Dependent variable The dependent variable is the variable that you measure or observe. The dependent variable gets its name because it is the factor that is dependent on the state of the independent variable. Example: In the experiment measuring the effect of temperature on solubility, solubility would be the dependent variable. Controlled variable A controlled variable or constant variable is a variable that does not change during an experiment. Example: In the experiment measuring the effect of temperature on solubility, controlled variable could include the source of water used in the experiment, the size and type of containers used to mix chemicals, and the amount of mixing time allowed for each solution. Extraneous Variables Extraneous variables are "extra" variables that may influence the outcome of an experiment, but aren't taken into account during measurement. Ideally, these variables won't impact the final conclusion drawn by the experiment, but they may introduce error into scientific results. If you are aware of any extraneous variables, you should enter them in your lab notebook. Examples of extraneous variables include accidents, factors you either can't control or can't measure, or factors you consider unimportant. Every experiment has extraneous variables. Example: You are conducting an experiment to see which paper airplane design flies longest. You may consider the color of the paper to be an extraneous variable. You note in your lab book that different colors of papers were used. Ideally, this variable does not affect your outcome. Difference Between a Control Group and Experimental Group An experimental group is the group in a scientific experiment where the experimental procedure is performed. This group is exposed to the independent variable being tested and the changes observed and recorded. A control group is a group separated from the rest of the experiment where the independent variable being tested cannot influence the results. This isolates the independent variable's effects on the experiment and can help rule out alternate explanations of the experimental results. Experiments that use control groups are called controlled experiments. Oct 2 9:34 AM 7

8 Dimensional Analysis Problem solving method used to convert between units or dimensions of measure Requires a relationship between units of measure called conversion factors How would you convert 10 years to... 1) days? 2) minutes? 3) seconds? You are using dimensional analysis in this process! Sometimes, you may not even understand or know the unit or dimension, but as long as you have the conversion factor (relationship between the units), you can solve using dimensional analysis: 1 jib jab = 14 joots How many kips are in 60 3 joots = 5 larks jib jabs? 1 lark = 16 milos 2 milos = 7 kips Oct 7 8:07 AM 8

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11 Measurement Stations Review Answers 1) 1 pt: 10 mm = 1 cm 2) 2 pt: 16 cm = km 3) 3 pt: 0.25 Mm = nm 4) 1 pt: Density = 3.50 g/0.95 ml = 3.68 g/ml 5) 2 pt: Mass = 1.48 g/ml X 25.0 ml = 37.0 g 6) 3 pt: 3.5 cm X 5 cm X 1.78 cm = cm cm 3 X 2.79 g/cm 3 = g 7) 1 pt: Precise since they are grouped together but not close to the actual value. 8) 2 pt: Mean = 1.96 g/cm 3 % error = [ ]/1.79 X 100 = 9.5% 9) 3pt: Mean = 1.96 g/cm 3 Deviations: [ ] = 0.03 [ ] = 0.05 [ ] = 0.09 Average Deviation = /3 = 0.06 g/cm 3 10) 1 pt: g = 2.5 X 10 4 g cm = X 10 6 cm 11) 2 pt: g / ml = g/ml = 8.0 X 10 2 g/ml 12) 3 pt: 1.24 X 10 3 / 2.0 X 10 2 = 1240 / = g/ml = 6.2 X 10 4 g/ml (5.81 X 10 3 )(6.94 X 10 1 ) = 5850 X = = X 10 3 Oct 17 2:27 PM 11

12 Scientific Notation Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing , we write 5.6 x So, how does this work? We can think of 5.6 x 10 9 as the product of two numbers: 5.6 (the digit term) and 10 9 (the exponential term). Here are some examples of scientific notation = 1 x = x = 1 x = x = 1 x = 4.82 x = 1 x = 8.9 x 10 1 (not usually done) 1 = /10 = 0.1 = 1 x = 3.2 x 10 1 (not usually done) 1/100 = 0.01 = 1 x = 5.3 x /1000 = = 1 x = 7.8 x /10000 = = 1 x = 4.4 x 10 4 As you can see, the exponent of 10 is the number of places the decimal point must be shifted to give the number in long form. A positive exponent shows that the decimal point is shifted that number of places to the right. A negative exponent shows that the decimal point is shifted that number of places to the left. In scientific notation, the digit term indicates the number of significant figures in the number. The exponential term only places the decimal point. As an example, = 4.66 x 10 7 This number only has 3 significant figures. The zeros are not significant; they are only holding a place. As another example, = 5.3 x 10 4 This number has 2 significant figures. The zeros are only place holders. How to do Scientific Notation on calculator: On your scientific calculator: Make sure that the number in scientific notation is put into your calculator correctly. Read the directions for your particular calculator. For inexpensive scientific calculators: Punch the number (the digit number) into your calculator. Push the EE or EXP button. Do NOT use the x (times) button!! Enter the exponent number. Use the +/ button to change its sign. Voila! Treat this number normally in all subsequent calculations. To check yourself, multiply 6.0 x 10 5 times 4.0 x 10 3 on your calculator. Your answer should be 2.4 x Oct 9 2:11 PM 12

13 Significant Figures Rules Significant figures are critical when reporting scientific data because they give the reader an idea of how well you could actually measure/report your data. Before looking at a few examples, let's summarize the rules for significant figures. 1) ALL non zero numbers (1,2,3,4,5,6,7,8,9) are ALWAYS significant. 2) ALL zeroes between non zero numbers are ALWAYS significant. 3) ALL zeroes which are SIMULTANEOUSLY to the right of the decimal point AND at the end of the number are ALWAYS significant. 4) ALL zeroes which are to the left of a written decimal point and are in a number >= 10 are ALWAYS significant. A helpful way to check rules 3 and 4 is to write the number in scientific notation. If you can/must get rid of the zeroes, then they are NOT significant. Examples: How many significant figures are present in the following numbers? Number # Significant Figures Rule(s) 48, ,2, , , ,2,3,4 3,000, ,3,4 Oct 9 1:58 PM 13

14 SIGNIFICANT FIGURES Mathematical Operations ADDITION AND SUBTRACTION: When adding or subtracting numbers, count the NUMBER OF DECIMAL PLACESto determine the number of significant figures. The answer cannot CONTAIN MORE PLACES AFTER THE DECIMAL POINT THAN THE SMALLEST NUMBER OF DECIMAL PLACESin the numbers being added or subtracted. Example: (6 places after the decimal point) (4 places after the decimal point) (2 places after the decimal point) (on calculator) (rounded to 2 places in the answer) MULTIPLICATION AND DIVISION: When multiplying or dividing numbers, count the NUMBER OF SIGNIFICANT FIGURES. The answer cannot CONTAIN MORE SIGNIFICANT FIGURES THAN THE NUMBER BEING MULTIPLIED OR DIVIDED with the LEAST NUMBER OF SIGNIFICANT FIGURES. Example: (8 significant figures) x (5 significant figures) (on calculator) (rounded to 5 significant figures) Oct 9 2:03 PM 14