Chapter 2:  Data Analysis Section 1:  Units of measurement
Intro problems:  D = m   V <ul><li>Calculate the density of a piece of bone with a mass of 3.8 g and a volume of 2.0 cm 3 ...
Not so long ago……. <ul><li>People used all kinds of units to describe measurements: </li></ul><ul><li>Their feet </li></ul...
Needless to say, this led to much confusion! <ul><li>Scientist needed a way to report their findings in a way that everyon...
SI Units <ul><li>A system of standard measures that every scientist uses </li></ul><ul><li>It consists of 7 base units whi...
SI Base Units Quantity Base unit Time second (s) Length meter (m) Mass kilogram (kg) Temperature kelvin (K) Amount of subs...
Time <ul><li>Base unit for time is the second </li></ul><ul><li>It is based on the frequency of microwave radiation given ...
Length <ul><li>The SI unit for length is the meter (m). </li></ul><ul><li>The distance that light travel through a vacuum ...
Mass <ul><li>Base unit for mass is the kilogram (kg) </li></ul><ul><li>You may see grams (g) or milligrams (mg) </li></ul>...
Temperature <ul><li>You classify an object as hot or cold by whether heat flows from you to the object or from the object ...
<ul><li>In science, the celsius and kelvin scales are most often used. </li></ul><ul><li>To convert from celsius to kelvin...
Derived Units <ul><li>Not all quantities can be measured with base units </li></ul><ul><li>Volume —the space occupied by a...
<ul><li>Density — a ratio that compares the mass of an object to its volume </li></ul><ul><li>--units are grams per cubic ...
Example:  If a sample of aluminum has a mass of 13.5g and a volume of 5.0 cm 3 , what is its density? Density =  mass   vo...
Suppose a sample of aluminum is placed in a 25 ml graduated cylinder containing 10.5 ml of water.  A piece of aluminum is ...
Practice Problems—pg. 29 # 1, 2, 3
Other Derived Quantities <ul><li>Velocity  or speed-  distance an obj travels over a period of time </li></ul><ul><ul><li>...
Metric Prefixes <ul><li>To better describe the range of possible measurements, scientists add prefixes to the base units. ...
Converting Between Units <ul><li>To convert b/w units simply move the decimal place to the right or left depending on the ...
Section 2.2 Scientific Notation and Dimensional Analysis
Scientific Notation <ul><li>A way to handle very large or very small numbers </li></ul><ul><li>Expresses numbers as a mult...
Change the following data into scientific notation. a.  The diameter of the sun is 1 392 000 km. b.  The density of the su...
Practice probs. Pg. 32  #12, 13
To add or subtract in scientific notation: <ul><li>The exponents must be the same before doing the arithmetic </li></ul><u...
Practice probs. Pg. 32  #14
To multiply or divide numbers in scientific notation: <ul><li>To  multiply :  multiply the numbers and  ADD  the  exp onen...
<ul><li>To  divide :  divide the numbers and  SUBTRACT  the  exp onents </li></ul><ul><li>ex:  (9 x 10 8 )    (3 x 10 -4 ...
Practice probs. Pg. 33  #15, 16
Dimensional analysis <ul><li>A method of problem-solving that focuses on the units used to describe matter </li></ul><ul><...
<ul><li>To use  conversion factors  simply write: </li></ul><ul><ul><li>The  number  given with the  unit   </li></ul></ul...
Practice: Convert 360 L to ml and to teaspoons:
<ul><li>How many seconds are there in 24 hours? </li></ul><ul><li>How many seconds are there in 2 years? </li></ul>
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? HINTs: Co...
Section 2.3 How reliable are measurements:
Sometimes an estimate is acceptable and sometimes it is not. <ul><li>When you are driving to the beach </li></ul><ul><li>M...
When scientists make measurements, they evaluate the  accuracy  and  precision  of the measurements. <ul><li>Accuracy —how...
<ul><li>Precision —how close a  series  of measurements are to each other </li></ul>Not precise Precise
Density Data collected by 3 different students Which student is the most accurate?  Which is most precise?  What could cau...
It is important to calculate the difference between an accepted value and an experimental value. <ul><li>To do this, you c...
Calculate the percent error for Student A Percent error =  error  x  100   accepted value First, you must calculate the er...
Practice probs. Pg. 38 #29
Significant Figures <ul><li>Scientists indicate the precision of measurements by the number of digits they report (digits ...
<ul><li>There are 2 different types of numbers </li></ul><ul><ul><li>Exact </li></ul></ul><ul><ul><li>Measured </li></ul><...
Learning Check <ul><li>Classify each of the following as an exact or a </li></ul><ul><li>measured number. </li></ul><ul><u...
<ul><li>Classify each of the following as an exact (1) or a </li></ul><ul><li>measured(2) number.  </li></ul><ul><li>This ...
Measurement and Significant Figures <ul><li>Every experimental measurement has a degree of uncertainty. </li></ul><ul><li>...
What is the Length? <ul><li>We can see the markings between 1.6-1.7cm </li></ul><ul><li>We can’t see the markings between ...
Learning Check What is the length of the wooden stick? 1)  4.5 cm  2)  4.54 cm  3)  4.547 cm
Measured Numbers <ul><li>Do you see why Measured Numbers have error…you have to make that Guess! </li></ul><ul><li>All but...
Rules for significant figures <ul><li>Non-zero numbers are always significant  72.3 g has__  </li></ul><ul><li>Zeros betwe...
Determine the number of significant figures in the following masses: a.  0.000 402 30 g b.  405 000 kg a.  0.000 402 30 g ...
To check, write the number in scientific notation <ul><li>Ex:  0.000 402 30  becomes </li></ul>4.0230 x 10 -4 and has  5  ...
Practice probs. Pg. 39 # 31, 32
Rounding to a specific # of sig figs <ul><li>When rounding to a specific place using sig figs, use the rounding rules you ...
Practice probs. Pg. 41 #34
Calculations and Sig Figs <ul><li>Adding/ Subtracting: </li></ul><ul><ul><li>Keep the least amount of sig fig in the decim...
Calculations and Sig Figs <ul><li>Follow your sig figs through the problem, but round at the end </li></ul><ul><ul><li>Ex:...
Practice probs. Pg. 41 # 35, 36 pg. 42  #37, 38
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Ch 2 data analysis

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

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