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Chapter 2: Data Analysis     Section 1: Units     of measurement
Intro problems: D = m                            V• Calculate the density of a piece of bone  with a mass of 3.8 g and a v...
Not so long ago…….People used all kinds of units to describe  measurements: Their feet Sundials The length of their arm
Needless to say, this led to much           confusion!• Scientist needed a way to report their  findings in a way that eve...
SI Units A system of standard measures that every  scientist uses It consists of 7 base units which have real  measures ...
SI     UnitsBase    Quantity            Base unitTime                second (s)Length              meter (m)Mass          ...
Time Base unit for time is the second It is based on the frequency of microwave  radiation given off by a cesium-133 atom
Length The SI unit for length is  the meter (m). The distance that light  travel through a vacuum Equals 1/300,000,000 ...
MassBase unit for mass is the kilogram (kg)You may see grams (g) or milligrams (mg)Defined by a platinum- iridium cylin...
Temperature You classify an object as  hot or cold by whether  heat flows from you to the  object or from the object  to ...
Temperature In science, the celsius and kelvin scales are most  often used. To convert from celsius to kelvin: add 273  ...
Der ived Unit s Not all quantities can be   measured with base unitsVolume—the space occupied by   an object   -measured ...
Der ived Unit sDensity—a ratio that compares the mass of an  object to its volume--units are grams per cubic centimeter (g...
Example: If a sample of aluminum has a mass of 13.5g and a volume of 5.0 cm3,          what is its density?Density = mass ...
Suppose a sample of aluminum is placed in a 25 mlgraduated cylinder containing 10.5 ml of water. Apiece of aluminum is pla...
Practice Problems—pg. 29 # 1, 2, 3
Other Derived Quantities• Velocity or speed- distance an obj travels over a  period of time  – V = ∆d/ t  – Units: m/s• Fo...
Metric Prefixes• To better describe the range of possible  measurements, scientists add prefixes to the base  units.• For ...
Converting Between Units• To convert b/w units simply move the decimal  place to the right or left depending on the  numbe...
Section 2.2Scientific Notation and Dimensional Analysis
Scientific Notation• A way to handle very large or very small  numbers• Expresses numbers as a multiple of 10 factors• Str...
Change the following data into scientific notation.a. The diameter of the sun is 1 392 000 km.b. The density of the sun’s ...
Practice probs. Pg. 32 #12, 13
To add or subtract in scientific notation:+ The exponents must be the same before doing the  arithmetic+ Add/Subtract numb...
Practice probs. Pg. 32 #14
To multiply or divide numbers in          scientific notation:To multiply: multiply the numbers and ADD the exponents    ...
To multiply or divide numbers in          scientific notation:To divide: divide the numbers and SUBTRACT the exponents   ...
Practice probs. Pg. 33 #15, 16
Dimensional analysis• A method of problem-solving that focuses on the  units used to describe matter• Converts one unit to...
Dimensional analysis                      cont….• To use conversion factors simply write:  1. The number given with the un...
Practice: Convert 360 L to ml      and to teaspoons:
1. How many seconds are there in           24 hours?2. How many seconds are there in 2              years?
Practice probs. Pg. 34 #17, 18
You can convert more than one unit at a time: What is a speed of 550 meters per second in kilometers per minute?      HINT...
Section 2.3How reliable are measurements:
Sometimes an estimate is acceptable and         sometimes it is not.                                      Okay? When you ...
When scientists make measurements, they evaluatethe accuracy and precision of the measurements. Accuracy—how close a meas...
 Precision—how close a series of   measurements are to each otherNot precise                     Precise
Density Data collected by 3 different studentsAccepted density  of Sucrose =     Student A Student B Student C   1.59 g/cm...
It is important to calculate the difference       between an accepted value and an             experimental value. To do ...
Calculate the percent error for                      Student APercent error =   error        x 100              accepted v...
Practice probs. Pg. 38 #29
Significant Figures Scientists indicate the precision of  measurements by the number of digits they  report (digits that ...
Significant Figures There are 2 different types of numbers   o Exact   o Measured Exact numbers are infinitely important...
Learning CheckClassify each of the following as an exact or ameasured number.  1 yard = 3 feet  The diameter of a red bloo...
SolutionClassify each of the following as an exact (1) or ameasured(2) number.This is a defined relationship.A measuring t...
Measurement and Significant                  Figures•        Every experimental         measurement has a degree of       ...
What is the Length?•    We can see the markings between 1.6-1.7cm•    We can’t see the markings between the .6-.7•    We m...
Learning CheckWhat is the length of the wooden stick?      1) 4.5 cm      2) 4.54 cm      3) 4.547 cm
Measured Numbers• Do you see why Measured Numbers have  error…you have to make that Guess!• All but one of the significant...
Rules for significant figures1.   Non-zero numbers are always significant      72.3 g has__2.   Zeros between non-zero num...
Determine the number of significant figures inthe following masses:a. 0.000 402 30 gb. 405 000 kga. 0.000 402 30 g        ...
To check, write the number in scientific               notationEx: 0.000 402 30   becomes           4.0230 x 10-4   and ha...
Practice probs. Pg. 39 # 31, 32
Rounding to a specific # of sig figsWhen rounding to a specific place using sig figs, use the rounding rules you already k...
Practice probs. Pg. 41 #34
Calculations and Sig Figs• Adding/ Subtracting:  – Keep the least amount of sig fig in the decimal    portion only.  – Ex:...
Calculations and Sig Figs• Follow your sig figs through the problem,  but round at the end  – Ex: (3.94 x 2.1) + 2.3418/ ....
Practice probs. Pg. 41 # 35, 36        pg. 42 #37, 38
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Transcript of "Ch 2 data analysis"

  1. 1. Chapter 2: Data Analysis Section 1: Units of measurement
  2. 2. Intro problems: D = m V• Calculate the density of a piece of bone with a mass of 3.8 g and a volume of 2.0 cm3• A spoonful of sugar with a mass of 8.8 grams is poured into a 10 mL graduated cylinder. The volume reading is 5.5 mL. What is the density of the sugar?
  3. 3. Not so long ago…….People used all kinds of units to describe measurements: Their feet Sundials The length of their arm
  4. 4. Needless to say, this led to much confusion!• Scientist needed a way to report their findings in a way that everyone else understood.• So, in 1795, the French developed a system of standard units, which was updated in 1960• The revised system is called the Système Internationale d’Unités, which is abbreviated SI
  5. 5. SI Units A system of standard measures that every scientist uses It consists of 7 base units which have real measures in the real world
  6. 6. SI UnitsBase Quantity Base unitTime second (s)Length meter (m)Mass kilogram (kg)Temperature kelvin (K)Amount of substance mole (mol)Electric current ampere (A)Luminous intensity candela (cd)
  7. 7. Time Base unit for time is the second It is based on the frequency of microwave radiation given off by a cesium-133 atom
  8. 8. Length The SI unit for length is the meter (m). The distance that light travel through a vacuum Equals 1/300,000,000 of a second About 39 inches
  9. 9. MassBase unit for mass is the kilogram (kg)You may see grams (g) or milligrams (mg)Defined by a platinum- iridium cylinder stored in a bell jar in FranceAbout 2.2 pounds
  10. 10. Temperature You classify an object as hot or cold by whether heat flows from you to the object or from the object to you. Heat flows from hot to cold. Thermometers are used to measure temp. SI unit of temp is kelvin (K)
  11. 11. Temperature In science, the celsius and kelvin scales are most often used. To convert from celsius to kelvin: add 273 ex: -39º C + 273 = 234 K To convert from kelvin to celsius: subtract 273 ex: 332 K – 273 = 59ºC
  12. 12. Der ived Unit s Not all quantities can be measured with base unitsVolume—the space occupied by an object -measured in cubic meters (cm3) -or liters (L) or milliliters (ml)
  13. 13. Der ived Unit sDensity—a ratio that compares the mass of an object to its volume--units are grams per cubic centimeter (g/cm 3) D = m Density equals V mass divided by volume.
  14. 14. Example: If a sample of aluminum has a mass of 13.5g and a volume of 5.0 cm3, what is its density?Density = mass volume D= 13.5 g 5.0 cm3 D = 2.7 g/cm3
  15. 15. Suppose a sample of aluminum is placed in a 25 mlgraduated cylinder containing 10.5 ml of water. Apiece of aluminum is placed in the cylinder and the level of the water rises to 13.5 ml. The density of aluminum is 2.7 g/cm3. What is the mass of the aluminum sample?
  16. 16. Practice Problems—pg. 29 # 1, 2, 3
  17. 17. Other Derived Quantities• Velocity or speed- distance an obj travels over a period of time – V = ∆d/ t – Units: m/s• Force – push or a pull exerted on an object – F = m*a m= mass a= acceleration – Units: Kg * m/s2 = Newton (N)
  18. 18. Metric Prefixes• To better describe the range of possible measurements, scientists add prefixes to the base units.• For example: 3,000 m = 3 km (easier to manage)• Most common prefixes: – King Henry Died by Drinking Chocolate Milk• Metric prefixes are based on the decimal system
  19. 19. Converting Between Units• To convert b/w units simply move the decimal place to the right or left depending on the number of units jumped.• Ex: K he da base d c m – 24.56 m = 245.6 dm = 2,4560 mm• May use power of 10 to multiply or divide – Big units to small units Multiply – Small units to big units divide
  20. 20. Section 2.2Scientific Notation and Dimensional Analysis
  21. 21. Scientific Notation• A way to handle very large or very small numbers• Expresses numbers as a multiple of 10 factors• Structure: a number between 1 and 10; and ten raised to a power, or exponent – Positive exponents, number is > 1 – Negative exponents, number is <1 Ex: 300,000,000,000 written in scientific notation is 3.0 x 10 11
  22. 22. Change the following data into scientific notation.a. The diameter of the sun is 1 392 000 km.b. The density of the sun’s lower atmosphere is0.000 000 028 g/cm3.
  23. 23. Practice probs. Pg. 32 #12, 13
  24. 24. To add or subtract in scientific notation:+ The exponents must be the same before doing the arithmetic+ Add/Subtract numbers, keep the power of 10. Move the decimal to right (make # bigger): subtract from exponent (exp smaller) Ex: To add the numbers Move the decimal to left 2.70 x 107 (smaller #): add to exponent (bigger exp) 15.5 x 106 0.165 x 108
  25. 25. Practice probs. Pg. 32 #14
  26. 26. To multiply or divide numbers in scientific notation:To multiply: multiply the numbers and ADD the exponents ex: (2 x 103) x (3 x 102) 2x3=6 3+2=5 Answer = 6 x 105
  27. 27. To multiply or divide numbers in scientific notation:To divide: divide the numbers and SUBTRACT the exponents ex: (9 x 108) ÷ (3 x 10-4) 9÷3=3 8 – (-4) = 12 Answer = 3 x 1012
  28. 28. Practice probs. Pg. 33 #15, 16
  29. 29. Dimensional analysis• A method of problem-solving that focuses on the units used to describe matter• Converts one unit to another using conversion factors in a fraction format – 1teaspoon = 5 mL  1 tsp or 5 ml 5 ml 1 tsp – 1 km = 1000 m  1 km or 1000 m 1000 m 1 km
  30. 30. Dimensional analysis cont….• To use conversion factors simply write: 1. The number given with the unit 2. Write times and a line (x ______). 3. Place the unit you want to cancel on the bottom. 4. Use a conversion factor that contains that unit 5. Use as many conversion factors until you reach your answer Conversion factor – ex: Convert 48 km to meters: 1km = 1000 m 48 km x 1000m 1km = 48,000 m
  31. 31. Practice: Convert 360 L to ml and to teaspoons:
  32. 32. 1. How many seconds are there in 24 hours?2. How many seconds are there in 2 years?
  33. 33. Practice probs. Pg. 34 #17, 18
  34. 34. You can convert more than one unit at a time: What is a speed of 550 meters per second in kilometers per minute? HINTs:Convert one unit at a time! Units MUST be ACROSS from each other to cancel out!
  35. 35. Section 2.3How reliable are measurements:
  36. 36. Sometimes an estimate is acceptable and sometimes it is not. Okay? When you are driving to the beach Miles per gallon your car gets Your final grade in Chemistry X
  37. 37. When scientists make measurements, they evaluatethe accuracy and precision of the measurements. Accuracy—how close a measured value is to an accepted value. Not accurate Accurate
  38. 38.  Precision—how close a series of measurements are to each otherNot precise Precise
  39. 39. Density Data collected by 3 different studentsAccepted density of Sucrose = Student A Student B Student C 1.59 g/cm 3Trial 1 1.54 g/cm3 1.40 g/cm3 1.70 g/cm3Trial 2 1.60 g/cm3 1.68 g/cm3 1.69 g/cm3Trial 3 1.57 g/cm3 1.45 g/cm3 1.71 g/cm3Average 1.57 g/cm3 1.51 g/cm3 1.70 g/cm3 Which student is the most accurate? Which is most precise? What could cause the differences in data?
  40. 40. It is important to calculate the difference between an accepted value and an experimental value. To do this, you calculate the ERROR in data. (experimental – accepted) Percent error is the ratio of an error to an accepted value Percent error = error x 100 accepted value
  41. 41. Calculate the percent error for Student APercent error = error x 100 accepted value Density Accepted Error Trial value (g/cm3) (g/cm3) First, you must 1 1.54 1.59 calculate the error!! 2 1.60 1.59 Error = (experimental – accepted) 3 1.57 1.59
  42. 42. Practice probs. Pg. 38 #29
  43. 43. Significant Figures Scientists indicate the precision of measurements by the number of digits they report (digits that are DEPENDABLE) Include all known digits and one estimated digit. A value of 3.52 g is more precise than a value of 3.5 g A reported chemistry test score of 93 is more precise than a score of 90
  44. 44. Significant Figures There are 2 different types of numbers o Exact o Measured Exact numbers are infinitely important o Counting numbers : 2 soccer balls or 4 pizzas o Exact relationships, predefined values 1 foot = 12 inches , 1 m = 100 cm Measured number = they are measured with a measuring device (name all 4) so these numbers have ERROR. When you use your calculator your answer can only be as accurate as your worst measurement 
  45. 45. Learning CheckClassify each of the following as an exact or ameasured number. 1 yard = 3 feet The diameter of a red blood cell is 6 x 10-4 cm. There are 6 hats on the shelf. Gold melts at 1064°C. 45
  46. 46. SolutionClassify each of the following as an exact (1) or ameasured(2) number.This is a defined relationship.A measuring tool is used to determine length.The number of hats is obtained by counting.A measuring tool is required. 46
  47. 47. Measurement and Significant Figures• Every experimental measurement has a degree of uncertainty.• The volume, V, at right is certain in the 10’s place, 10mL<V<20mL• The 1’s digit is also certain, 17mL<V<18mL• A best guess is needed for the tenths place.• This guess gives error in 47 data. Chapter Two
  48. 48. What is the Length?• We can see the markings between 1.6-1.7cm• We can’t see the markings between the .6-.7• We must guess between .6 & .7• We record 1.67 cm as our measurement•48 The last digit an 7 was our guess...stop there
  49. 49. Learning CheckWhat is the length of the wooden stick? 1) 4.5 cm 2) 4.54 cm 3) 4.547 cm
  50. 50. Measured Numbers• Do you see why Measured Numbers have error…you have to make that Guess!• All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimate.• To indicate the precision of a measurement, the value recorded should use all the digits known with certainty.50
  51. 51. Rules for significant figures1. Non-zero numbers are always significant 72.3 g has__2. Zeros between non-zero numbers are 60.5 g has__ significant3. Leading zeros are NOT significant 0.0253 g has __ Leading zeros4. Trailing zeros are significant after a 6.20 g has__ number with a decimal point Trailing zeros 100 g has__
  52. 52. Determine the number of significant figures inthe following masses:a. 0.000 402 30 gb. 405 000 kga. 0.000 402 30 g 5 sig figs b. 405 000 kg 3 sig figs
  53. 53. To check, write the number in scientific notationEx: 0.000 402 30 becomes 4.0230 x 10-4 and has 5 significant figures
  54. 54. Practice probs. Pg. 39 # 31, 32
  55. 55. Rounding to a specific # of sig figsWhen rounding to a specific place using sig figs, use the rounding rules you already know. 1 2 3 4 ex: Round to 4 sig figs: 32.5432 1. Count to four from left to right: 2. Look at the number to the right of the 4th digit and apply 32.54 rounding rules
  56. 56. Practice probs. Pg. 41 #34
  57. 57. Calculations and Sig Figs• Adding/ Subtracting: – Keep the least amount of sig fig in the decimal portion only. – Ex: a. 0.011 + 2.0 = b. 0.020 + 3 + 5.1 =• Multiplying/ Dividing: – Keep the least amount of sig figs total – Ex: a. 270/3.33 = b. 2.3 x 100 =
  58. 58. Calculations and Sig Figs• Follow your sig figs through the problem, but round at the end – Ex: (3.94 x 2.1) + 2.3418/ .004
  59. 59. Practice probs. Pg. 41 # 35, 36 pg. 42 #37, 38
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