2.2 Scientific Notation & Dimensional Analysis. Monday, September 23, 13

Transcription

1 2.2 Scientific Notation & Dimensional Analysis

2 Scientific Notation Can be used to express any number as a number between 1 and 10 (coefficient) multiplied by 10 raised to any power (exponent). 36,000 = 3.6 x 104 Positive exponent = how much the coefficient must be multiplied by = 3.6 x 10-4

3 Scientific Notation The value of the exponent = the number of places the decimal point moved. Exponent is positive when decimal point moves to the left. EXAMPLES Exponent is negative when the decimal point moves to the right. EXAMPLES

4 Math with Scientific Notation Addition and Subtraction Exponents must be the same. EXAMPLES If not the same, rewrite with same exponent. EXAMPLES

5 Scientific Notation Multiplication & Division Two-step process. Multiply / divide coefficients. Add / subtract exponents EXAMPLES

6 Dimensional Analysis Use conversion factors to to convert one unit to another. Conversion factor is a ratio of equivalent values having different units. Relationships between units EXAMPLES

7 Dimensional Analysis Use conversion factors to to convert one unit to another. Conversion factor is a ratio of equivalent values having different units. Prefixes are the source of many conversion factors Prefix Symb Numerical Conversion Factor Mega ol M 1,000,000 Value 1 Mg = 1,000,000 g Kilo K 1,000 1 Kg = 1,000 g Deci d dg = 1 g Centi c cg = 1 g Milli m mg = 1 g Micro u ,000,000 ug = 1 g

8 Using Conversion Factors Must accomplish two things: Must cancel one unit. Must introduce a new one. All units except what you want must cancel out. EXAMPLE How many pizzas do I need to order to give each person in class two pieces? (1 pizza = 8 pieces)

9 2.3 Uncertainty in Data

10 Uncertainty in Data Every measurement contains some amount of error. Must evaluate both accuracy and precision each time.

11 Uncertainty in Data Accuracy The closeness of a measured value to an accepted value. Precision The closeness a series of measurements are to one another.

12 Uncertainty in Data

13 Uncertainty in Data Which student is the most accurate? Student A Which student is the most precise? Student C

14 Error and Percent Error Accuracy of experiment is measured by comparing how close the experimental value comes to the accepted value. Experimental value Accepted value True value Measured during an experiment.

15 Error and Percent Error Experimental Error Difference between experimental and accepted values. Error = experimental value - accepted value Percent Error Expresses error as percentage of accepted value. Percent Error = error X 100 accepted value Accepted value= 1.59 Error = 0.05 Percent Error = 3.14%

16 2.4 Significant Figures

17 Significant Figures Precision is limited by the tools available. Indicated by the number of digits reported Significant figures include all known digits plus one estimated digit.

18 Significant Figures Rules for Significant Figures What is the measurement of the rod reported in significant figures?

19 Significant Figures Rules for Significant Figures What is the measurement of the rod reported in significant figures?

20 Significant Figures Rules for Significant Figures 1. All non zero numbers ARE significant 2. All zeros at the beginning of a number are NOT significant 3. All zeroes in between non zero numbers ARE significant 4. Zeroes at the end MAY OR MAY NOT be significant If there is a decimal point anywhere in the problem, it is significant If NO decimal point exists it is NOT significant.

21 to the correct number of significant figures. Significant Figures Rules for Significant Figures 1. All non zero numbers ARE significant 2. All zeros at the beginning of a number are NOT significant 3. All zeroes in between non zero numbers ARE significant 4. Zeroes at the end MAY OR MAY NOT be significant If there is a decimal point anywhere in the problem, it is significant If NO decimal point exists it is NOT significant. 1) = 4 2) 820,400.0 = 7 3) 807,000 = 3 4) = 5 6) = 2

22 to the correct number of significant figures. Significant Figures Rules for addition and subtraction The answer should have the same number of decimal places as the original value with the least number of decimal places (example: = 9.4) Practice complete each addition or subtraction problem and round the answer to the correct number of decimal places = = =

23 to the correct number of significant figures. Significant Figures Rules for multiplication and division The answer should have the same number of significant figures as the original value with the least number of significant figures (example: = 36) Practice - complete each multiplication or division problem and round the answer to the correct number of significant figures /.36 = 62.1 = 62 = = = = 16

24 Significant Figures Rounding Numbers Identify the last significant figure. If number to right of last significant figure is: Less than Five, DO NOT change: 35.3 = 35 Greater than FIVE, round UP: 35.8 = 36 Five: Do nothing if the last significant figure is EVEN: = 3.52 Round UP if the last significant figure is ODD: = 3.52

25 2.4 Representing Data

26 Representing Data A picture is worth... A graph is a picture Scientists use graphs to present data in a form that allows them analyze results and communicate information about their experiments.

27 Graphing Goal of experiments is to discover patterns within situations. Does changing temp change rate of rxn? Does change in diet affect rat s ability to navigate maze? Data listed in tables may not make patterns obvious. Using data to create graphs can help reveal patterns. Graph = visual display of data.

28 Circle Graphs (Pie Chart) Useful for showing parts of a fixed whole. Comparison of data Parts usually labeled as percents.

29 Circle Graphs (Pie Chart)

30 Circle Graphs (Pie Chart)

31 Bar Graphs Shows how quantities vary across categories. Include time, location, and temperature. Quantity being measured goes on y-axis. Which variable is this? Quantity that a scientist changes goes on x-axis. Which variable is this?

32 Bar Graphs

33 Line Graphs Type of graph most used in chemistry. Points represent the intersection of of data for two variables. Like a bar graph: independent variable = x-axis dependent variable = y-axis

34 Line Graphs Points represent the intersection of of data for two variables. Like a bar graph: independent variable = x-axis dependent variable = y-axis

35 Line Graphs Contain best-fit line. Line drawn such that equal number of points fall above and below line.

36 Line Graphs Contain best-fit line. Line drawn such that equal number of points fall above and below line.

37 Line Graphs If the best-fit line is straight, there is a linear relationship between variables. Directly related If the best-fit line is curved, there is a nonlinear relationship between variables. Inverse relationship

38 Line Graphs Slope of line tells HOW variables are related. Slope equation =

39 Line Graphs Slope of line tells HOW variables are related. Rising slope = positive slope. Both dependent and independent variable increase. Sinking slope = negative slope. Dependent variable decreases as independent variable increases.

40 Line Graph - Line Graphs Line Graph - Slope of line tells HOW variables are related

41 How to Interpret Graphs Determine independent and dependent variables. x-axis vs y-axis? Decide if relationship is linear or nonlinear. If linear, determine if slope is positive or negative.

42 Interpolation vs Extrapolation Connected points on line graph = continuous data. Reading values between recorded data points is called interpolation.

43 Interpolation vs Extrapolation Connected points on line graph = continuous data. Reading values between recorded data points is called interpolation. What is the temperature at an elevation of 350 m?

44 Interpolation vs Extrapolation Extending line beyond plotted points to estimate values for variables = extrapolation. Can lead to errors and inaccuracy.

45 Interpolation vs Extrapolation Extending line beyond plotted points to estimate values for variables = extrapolation. Can lead to errors and inaccuracy. What is the temperature at an elevation of 800 m?