1. Data Analysis Chapter 2

2. Units of Measurement Is a measurement useful without a unit? Is a measurement useful without a unit?

3. SI Units The metric system is used worldwide. The metric system is used worldwide. Long ago, inexact measurements were used. For example: Long ago, inexact measurements were used. For example: Boundaries would’ve been marked off by walking & counting the number of steps. Boundaries would’ve been marked off by walking & counting the number of steps. Time was measured with a sundial or an hourglass filled with sand. Time was measured with a sundial or an hourglass filled with sand.

4. SI Units The metric system was adopted in 1795 by a group of French scientists. The metric system was adopted in 1795 by a group of French scientists. In 1960, an international committee of scientists met to update the metric system. Called the SI system (Systeme Internationale d’Unites) In 1960, an international committee of scientists met to update the metric system. Called the SI system (Systeme Internationale d’Unites)

5. Base Units There are 7 base units in SI. A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world. There are 7 base units in SI. A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world. The base unit for: The base unit for: Time is second… electrical current is… Time is second… electrical current is… Length is meter… amount of sub is… Length is meter… amount of sub is… Mass is kilogram… luminosity is… Mass is kilogram… luminosity is… Temp is… Temp is… The prefixes used with SI units are …(table 2-2) The prefixes used with SI units are …(table 2-2)

6. Derived Units A derived unit is a unit that is defined by a combination of base units. A derived unit is a unit that is defined by a combination of base units. Example: speed is meters/second (m/s) Example: speed is meters/second (m/s) Get out your calculators! Get out your calculators!

7. Volume Volume is the space occupied by an object. Volume is the space occupied by an object. 1 L= 1 dm 3 1 mL= 1 cm 3 1 L= 1 dm 3 1 mL= 1 cm 3 You would use a graduated cylinder to measure the volume of a liquid in the lab. You would use a graduated cylinder to measure the volume of a liquid in the lab. You would measure length x width x height to find the volume of a “regular” solid. You would measure length x width x height to find the volume of a “regular” solid. How would you find the volume of an irregular solid? How would you find the volume of an irregular solid?

9. Density Density of a ratio that compares the mass of an object to its volume Density of a ratio that compares the mass of an object to its volume D=m/v D=m/v Ex 1 Calculate the density of a piece of aluminum that has the mass of 13.5g & a volume of 5.0cm 3. What is this substance? Ex 1 Calculate the density of a piece of aluminum that has the mass of 13.5g & a volume of 5.0cm 3. What is this substance?

11. Ex 2 Suppose a sample of aluminum (Al) is placed in a graduated cylinder containing 10.5 mL of water & rises to 13.5 mL. What is the mass of the aluminum sample? (Use the density from example 1) Ex 2 Suppose a sample of aluminum (Al) is placed in a graduated cylinder containing 10.5 mL of water & rises to 13.5 mL. What is the mass of the aluminum sample? (Use the density from example 1)

12. Density Density of a substance is a property that doesn’t change, UNLESS altered by an outside substance. Density of a substance is a property that doesn’t change, UNLESS altered by an outside substance. D water at STP is 0.998 g/cm 3 D water at STP is 0.998 g/cm 3 D water at 4°C is 1.00 g/cm 3 D water at 4°C is 1.00 g/cm 3 ** practice problems #1-3 ** practice problems #1-3

13. If we know the Density & dimensions of a cube, can we determine the mass of the cube? If we know the Density & dimensions of a cube, can we determine the mass of the cube? If the D air = 0.00122 g/cm 3, then what is the mass of air in this room? If the D air = 0.00122 g/cm 3, then what is the mass of air in this room?

14. Temperature Temperature is the measure of how hot/cold an object is relative to other objects. Temperature is the measure of how hot/cold an object is relative to other objects. Scales of temperature: Scales of temperature: Celsius- derived by Anders Celsius & used the point at which water freezes & boils to establish his scale Celsius- derived by Anders Celsius & used the point at which water freezes & boils to establish his scale Freezing point- 0° C Freezing point- 0° C Boiling point- 100° C Boiling point- 100° C

15. Temperature Kelvin (K)- derived by William Thomson, known as Lord Kelvin Kelvin (K)- derived by William Thomson, known as Lord Kelvin Kelvin is the SI base unit of temperature Kelvin is the SI base unit of temperature Conversion process of Celsius to Kelvin Conversion process of Celsius to Kelvin Add 273 Add 273 Conversion process of Kelvin to Celsius Conversion process of Kelvin to Celsius Subtract 273 Subtract 273 Ex. Ex.

16. **Practice problems 4-6 **Practice problems 4-6 4. Convert 357°C to Kelvin 5. Convert -39°C to Kelvin 6. Convert 266 K to Celsius

17. Scientific Notation Scientific notation- expresses a number as a number between 1 & 10 and then raised to a power, or exponent. Scientific notation- expresses a number as a number between 1 & 10 and then raised to a power, or exponent. When a number is more than one, the exponent is positive. When a number is more than one, the exponent is positive. If less than one, the exponent is negative. If less than one, the exponent is negative.

18. Scientific Notation How do we convert data into Sci. Not. ? Move the decimal until you have a number between 1 & 10. Move the decimal until you have a number between 1 & 10. The exponent in the number of times you moved the decimal. The exponent in the number of times you moved the decimal. Put unit with answer. Put unit with answer.

19. Scientific Notation ** Practice problems 1-8 ** Practice problems 1-8 1. 700 m 2. 38 000 m 3. 4 500 000m 4. 685 000 000 000 m

20. 5. 0.0054 kg 6. 0.000 006 87 kg 7. 0.000 000 076 kg 8. 0.000 000 000 8 kg

21. Calculations with Sci Not. How do we add/subtract using Scientific Notation? How do we add/subtract using Scientific Notation? Make sure exponents are the same. Make sure exponents are the same. If the exponent is too large, decrease it & move the decimal that many times to the right. If the exponent is too large, decrease it & move the decimal that many times to the right. If the exponent is too small, increase it & move the decimal that many places to the left. If the exponent is too small, increase it & move the decimal that many places to the left.

22. Calculations with Sci Not. Ex. What is 2.70 x 10 7 + 15.6 x 10 6 ? ** practice problems 5-8 ** practice problems 5-8

23. 5. 1.26x10 4 kg + 2.5x10 3 kg 6. 7.06x10 -3 kg + 1.2x10 -4 kg 7. 4.39x10 5 kg – 2.8x10 4 kg 8. 5.36x10 -1 kg – 7.40x10 -2 kg

24. Calculations with Sci Not. How do we multiply/divide using sci. not.? How do we multiply/divide using sci. not.? Multiply/divide the factors(aka coefficients) first. Multiply/divide the factors(aka coefficients) first. Multiplication Multiplication Add the exponents. Add the exponents. Division Division Subtract the exponent of the denominator from the exponent of the numerator. Subtract the exponent of the denominator from the exponent of the numerator.

25. Calculations with Sci Not. Ex.1 What is (2 x 10 3 ) x (3 x 10 2 ) Ex.1 What is (2 x 10 3 ) x (3 x 10 2 ) Ex. 2 What is (9 x 10 8 ) / (3 x 10 -4 ) Ex. 2 What is (9 x 10 8 ) / (3 x 10 -4 ) ** practice problems 9-16. ** practice problems 9-16.

26. 9. (4x10 2 cm)x(1x10 8 cm) 9. (4x10 2 cm)x(1x10 8 cm) 10. (2x10 -4 cm)x(3x10 2 cm) 10. (2x10 -4 cm)x(3x10 2 cm) 11. (3x10 1 cm)x(3x10 -2 cm) 11. (3x10 1 cm)x(3x10 -2 cm) 12. (1x10 3 cm)x(5x10 -1 cm) 12. (1x10 3 cm)x(5x10 -1 cm) 13. (6x10 2 g)/(2x10 1 cm 3 ) 13. (6x10 2 g)/(2x10 1 cm 3 ) 14. (8x10 4 g)/( 4x10 1 cm 3 ) 14. (8x10 4 g)/( 4x10 1 cm 3 ) 15. (9x10 5 g)/ (3x10 -1 cm 3 ) 15. (9x10 5 g)/ (3x10 -1 cm 3 ) 16. (4x10 -3 g)/(2x10 -2 cm 3 ) 16. (4x10 -3 g)/(2x10 -2 cm 3 )

27. Dimensional Analysis Dimensional analysis- method of problem- solving that focuses on the units used to describe matter; often uses conversion factors. Dimensional analysis- method of problem- solving that focuses on the units used to describe matter; often uses conversion factors. Conversion factor- ratio of equivalent values used to express the same quantity in different units. Conversion factor- ratio of equivalent values used to express the same quantity in different units. Ex 1 How many hours are in one year? Ex 1 How many hours are in one year?

28. Conversion Factors Giga Giga Mega Mega Kilo Kilo Hecto Hecto Deca Deca BASE BASE Deci Deci Centi Centi Milli Milli Micro Micro Nano Nano (Angstro) (Angstro) Pico Pico

29. Dimensional Analysis Ex. 1 How many meters are in 48 km? Practice: What conversion factor should be used for the following conversion? A. 360 s  ms B. 4800 g  kg C. 6800 cm  m

30. Practice using dimensional analysis 1.4.5 L = __________mL 2.0.095mg = ____________cg 3.9500 mm = ___________m 4.0.575 km = ___________m 5.100 cm = ___________mm

31. **Handout “Unit Conversion…”

32. Conversion Ex. 2 What is the speed of 550 meters per second in kilometers per minute? Ex. 2 What is the speed of 550 meters per second in kilometers per minute?

33. Practice 6) How many seconds are there in 24.0 hours? 86,400 s 86,400 s 7) the density of gold is 19.3 g/mL. What is gold’s density in decigrams per liter? 193,000dg/L 193,000dg/L 8) A car is travelling 90. kilometers per hour. What is the speed in miles per minute? (1 km=0.62 mi) 0.93 mi/min 0.93 mi/min

34. Reliability How reliable are measurements? How reliable are measurements? Accuracy & Precision: Accuracy & Precision: Accuracy- refers to how close a measured value is to an accepted value. Accuracy- refers to how close a measured value is to an accepted value. Precision- refers to how close a series of measurements are to one another. Precision- refers to how close a series of measurements are to one another.

35. Accuracy or precision

37. Percent Error Percent error- ratio of an error to an accepted value. Percent error- ratio of an error to an accepted value. % error= accepted(book value) – exp (you) x 100 accepted % error= accepted(book value) – exp (you) x 100 accepted % error= (error/accepted) x 100 % error= (error/accepted) x 100 Ignore the negative sign, only the amount of error matters. Ignore the negative sign, only the amount of error matters.

38. Percent Error Ex. You calculated the length of a steel pipe to be 5.2 m. The accepted length is 5.5 m. What is the percent error? Ex. You calculated the length of a steel pipe to be 5.2 m. The accepted length is 5.5 m. What is the percent error?

39. Practice #1 Practice #1 The accepted density for Cu is 8.96 g/mL. Calculate the percent error for the measurement 8.86 g/mL. The accepted density for Cu is 8.96 g/mL. Calculate the percent error for the measurement 8.86 g/mL. **Worksheet** **Worksheet**

40. Significant Figures Significant figures- include all known digits plus one estimated digit. Significant figures- include all known digits plus one estimated digit. Rules: Rules: 1. Non-zero numbers are always significant Ex. 72.3 Ex. 700 Ex. 72.3 Ex. 700 2. “Sandwich zeros” are significant. 60.5 60.5 809 809 30.07 30.07

41. Significant Figures 3. Final zeros after the decimal are significant. a) 6.20 b) 9.00 c) 92.0 d) 0.009200 4. “Place holding” zeros are not significant. e) 0.095 f) 300 g) 50 h) 30,000

42. Significant Figures You can convert to scientific notation to remove place holders. You can convert to scientific notation to remove place holders. 30,000 = 3 x 10 4 30,000 = 3 x 10 4 Example: Determine the number of sig figs in the following masses. Example: Determine the number of sig figs in the following masses. a) 0.000 402 30 g a) 0.000 402 30 g b) 405 000 kg b) 405 000 kg c) 8.20 x 10 7 c) 8.20 x 10 7 *** practice problems p39 # 31 & 32 *** practice problems p39 # 31 & 32

43. Rounding Off Numbers Rounding to 3 sig figs Rounding to 3 sig figs 2.5320  if the 4 th sig fig is <5, do not change the 3 rd sig fig. 2.5320  if the 4 th sig fig is <5, do not change the 3 rd sig fig. 2.5360  if the 4 th sig fig is =>5, then round the 3 rd sig fig up. 2.5360  if the 4 th sig fig is =>5, then round the 3 rd sig fig up. Examples: Examples: 55.845  (4 sf) 55.845  (4 sf) 32.065  (2 sf) 32.065  (2 sf) 87.62  (1 sf) 87.62  (1 sf) 36,549,555  (2 sf) 36,549,555  (2 sf)

44. Addition/subtraction with sig figs Your answer must have the same number of digits to the right of the decimal as the measurement with the FEWEST digits to the right of the decimal. Your answer must have the same number of digits to the right of the decimal as the measurement with the FEWEST digits to the right of the decimal. Ex. Add the following measurements: 28.0 cm, 23.538 cm, 25.68 cm. Ex. Add the following measurements: 28.0 cm, 23.538 cm, 25.68 cm.

45. ** practice problems ** practice problems

46. Multiplication/division w/ sig figs Your answer must have the same number of sig figs as the measurement with the fewest sig figs. Your answer must have the same number of sig figs as the measurement with the fewest sig figs. Ex. Calculate the volume of a rectangular object w/ the following dimensions: length= 3.65 cm, Ex. Calculate the volume of a rectangular object w/ the following dimensions: length= 3.65 cm, width= 3.2cm, width= 3.2cm, height= 2.05 cm. height= 2.05 cm.

47. Multiplication/division w/ sig figs **practice problems 7-14 **practice problems 7-14 Check old worksheets Check old worksheets **worksheet** **worksheet**

48. Representing Data Graph- visual display of data Graph- visual display of data Circle graph- usually used to represent percentages of something. Circle graph- usually used to represent percentages of something.

49. Representing Data Bar graph- often used to show how a quantity varies with factors such as time, location, or temperature. Bar graph- often used to show how a quantity varies with factors such as time, location, or temperature. Independent variable- located on the x-axis Independent variable- located on the x-axis Dependent variable- located on the y-axis Dependent variable- located on the y-axis

50. Bar Graph

51. Representing Data Line Graph- most often used in chemistry Line Graph- most often used in chemistry The points on a line graph represent the intersection of data for 2 variables. The points on a line graph represent the intersection of data for 2 variables. Independent variable- located on the x-axis. Independent variable- located on the x-axis. Dependent variable- located on the y-axis Dependent variable- located on the y-axis

52. Best fit line- line drawn so that as many points fall above the line as fall below it. Best fit line- line drawn so that as many points fall above the line as fall below it. Straight best fit- there is a linear relationship Straight best fit- there is a linear relationship The variables are directly related The variables are directly related Curved best fit- there is a nonlinear relationship. Curved best fit- there is a nonlinear relationship. The variables are inversely related The variables are inversely related

54. Interpreting Data First thing, ID the variables; independent & dependent First thing, ID the variables; independent & dependent Notice what measurements were taken Notice what measurements were taken Decide if the relationship of the variables is linear/nonlinear. Decide if the relationship of the variables is linear/nonlinear.