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Chapter 3 Scientific Measurement
A.  Qualitative Measurements B.  Quantitative Measurements - give results in  descriptive ,  non-numeric  form - give resu...
II.  Scientific Notation Def – Scientific notation is simply writing a    number as a  product of two numbers . Examples: ...
<ul><li>2 parts of a number: </li></ul><ul><li>Coefficient –  a number between 1 and 10 </li></ul><ul><li>Exponent –  10 r...
Calculations with Scientific Notation 1.  Multiplication and Division a.  Multiplying –  MULTIPLY  the coefficients   and ...
Calculations with Scientific Notation 2.  Addition and Subtraction Rule:  First the powers of 10  must be the same! Then j...
Calculations with Scientific Notation 2.  Addition and Subtraction Rule:  First the powers of 10  must be the same! Then j...
<ul><li>Practice Problems </li></ul><ul><li>4.5 x 10 8 2.  3.6 x 10 -4 x  2.0 x 10 5   ÷   1.2 x 10 5 </li></ul><ul><li>2....
II.  Accuracy, Precision, and Error A.  Accuracy  – The measure of how close a measurement is to the  accepted value . B. ...
The Dartboard Model Accuracy = Precision =  Accuracy = Precision =  Accuracy = Precision =  Low Low  Low High High High
C.  Error Def – The difference between the  experimental     value and the  accepted  value. Experimental Value  –  The va...
Sample Problem: James weighs a metal cylinder and finds it has a mass of 48.34 grams.  If the actual mass of the cylinder ...
D.  Percent Error Def –  The absolute value of the error divided    by the accepted value, multiplied by 100 - Compares th...
Steve and Martin each order bricks from a lumber yard.  Steve orders 500 bricks to build a wall, but the lumber yard only ...
II.  Significant Figures in Measurements Significant Figures  –  All the digits that are known    in a measurement, plus o...
4.13 *Note:  With all measuring tools, you are expected to  estimate one digit beyond  what you can actually see marked = ...
Reporting Measurements in proper Sig Figs - Measurements must be reported with the  correct number of significant figures ...
Rules for Sig Figs (Rules for Zero’s) 1.  All nonzero digits  ARE  significant. 2.  Zero’s appearing between nonzero digit...
Rules for Sig Figs (Rules for Zero’s) 4.  Zeros at the end of a number and to the right of a decimal  ARE ALWAYS  signific...
V.  Significant Figures in Calculations General Rule : Your answer cannot be  more precise than the    measurements used t...
1.  Rounding  – Calculations must be rounded to make them consistent with the  measurements from which they were calculate...
c.  Identify the digit  immediately to the right   of the last significant figure: <ul><li>If it is less than 5 it is  dro...
2.  Addition and Subtraction Rule: The answer should be rounded to have the same number of  places after the decimal  as t...
3.  Multiplication and Division Rule: Round your answer to have the same number of  significant figures  as the measuremen...
VI.  International System of Units - Abbreviated  SI , after the French name, Le Syst é me International d’Unit é s - A re...
3 main base units: a.  Length =  meter (m) b.  Volume =  liter (L) c.  Mass =  gram (g)
Metric Prefixes:  ( Memorize!) giga- G 1,000,000,000x larger 10 9 mega- M 1,000,000x larger 10 6 kilo- k 1,000x larger 10 ...
Examples: 1 kilogram =  10 3  grams (1000x larger) 1 millimeter =  10 -3  meter (1000x smaller) 1 hectoliter =  10 2  lite...
10 birds = 1 meter Each bird = 1/10 th  of a meter (10 -1  m) 1 bird = 1 decimeter (1 dm) Example: 1 meter stick
2.  Measurements A.  Length – measure of  linear distance - Unit =  meters (m) Associations: 1 meter     1 yard  (39.5 in...
B.  Volume  –  the amount of space an    object takes up <ul><li>Units =  cubic meters (m 3 ) </li></ul><ul><ul><ul><li>li...
Ways to Measure Volume 1.  Geometric Solid  – (cube, rectangular solid, pyramid, cylinder, sphere, etc…) -  use an  equati...
Example 2:  Cylindrical Solid  (area of base x height) area of circle =   r 2 volume =   r 2 h * r = radius (1/2 the dia...
2.  Liquids  –  pour the liquid into a measured container (graduated cylinder) -  read the level of the meniscus in  liter...
3.  Irregular shaped solids  –  Water displacement ! -  Dunk an object in water and the water level  goes up ! 4.13 mL 4.7...
C.  Mass  – measures the quantity of matter an object contains <ul><li>SI unit – kilogram (kg) – standard! </li></ul><ul><...
1 kg = mass of 1 L of water at 4 degrees Celsius 1 kg = 2.2 lbs 1 ounce    28 grams 1 kg = 1000 grams 1 penny    3 grams
VII.  Temperature Definition – a measure of the  average kinetic energy  of particles in matter. -  Kinetic energy is ener...
-  Temperature also describes the  direction of heat flow  – from  hotter  to  colder a.  When you hold an ice cube it fee...
Temperature Scales: a.  Celsius scale – based on the  boiling and freezing points  of water b.  Kelvin scale – based on  a...
Fahrenheit =   F Celsius =   C Kelvin = K -273 0 100 -460 32 212 373 273 0 Freezing point of water Boiling point of wate...
The End
 
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Chapter 3 notes chemistry

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  1. 1. Chapter 3 Scientific Measurement
  2. 2. A. Qualitative Measurements B. Quantitative Measurements - give results in descriptive , non-numeric form - give results in definite form, numbers and units Examples: Mr. Smith is tall. The room is hot. Examples: Mr. Smith is 6 feet tall. The room is 70 degrees Fahrenheit.
  3. 3. II. Scientific Notation Def – Scientific notation is simply writing a number as a product of two numbers . Examples: 12,300,000 = _____________ 1.23 x 10 7 0.0000546 = _____________ 5.46 x 10 -5 .
  4. 4. <ul><li>2 parts of a number: </li></ul><ul><li>Coefficient – a number between 1 and 10 </li></ul><ul><li>Exponent – 10 raised to a power </li></ul>Note: Positive powers of 10 = large numbers (multiply) Negative powers of 10 = small numbers (divide) 3.6 x 10 4 = 3.6 x 10 x 10 x 10 x 10 = 36,000 8.1 x 10 -4 = 8.1 ÷ 10 ÷ 10 ÷ 10 ÷ 10 = 0.000 81 1.23 x 10 7 coefficient exponent
  5. 5. Calculations with Scientific Notation 1. Multiplication and Division a. Multiplying – MULTIPLY the coefficients and ADD the exponents. b. Dividing – DIVIDE the coefficients and SUBTRACT the exponents. Example 1: (9 x 10 4 ) x (2 x 10 3 ) 18 x 10 7 1.8 x 10 7 x 10 8 Example 2: (8 x 10 4 ) ÷ (2 x 10 7 ) 4 x 10 -3
  6. 6. Calculations with Scientific Notation 2. Addition and Subtraction Rule: First the powers of 10 must be the same! Then just add or subtract the coefficients and keep the power of 10 the same Example 1: (9 x 10 4 ) + (2 x 10 3 ) (9 x 10 4 ) ( 0.2 x 10 4 ) (0.2 x 10 4 ) 9.2 x 10 4 90 000 2 000 92 000
  7. 7. Calculations with Scientific Notation 2. Addition and Subtraction Rule: First the powers of 10 must be the same! Then just add or subtract the coefficients and keep the power of 10 the same Example 2: (4 x 10 8 ) - (9 x 10 6 ) (4 x 10 8 ) ( 0.09 x 10 8 ) (0.09 x 10 8 ) 3.91 x 10 8
  8. 8. <ul><li>Practice Problems </li></ul><ul><li>4.5 x 10 8 2. 3.6 x 10 -4 x 2.0 x 10 5 ÷ 1.2 x 10 5 </li></ul><ul><li>2.2 x 10 5 4. 6.07 x 10 12 + 5.5 x 10 6 – 4.3 x 10 11 </li></ul><ul><li>5. 6.02 x 10 23 6. 7.5 x 10 -5 x 2.00 x 10 -10 + 9.5 x 10 -8 </li></ul>
  9. 9. II. Accuracy, Precision, and Error A. Accuracy – The measure of how close a measurement is to the accepted value . B. Precision – How close a series of measurements are to each other . Note: Precision also describes how “ exact ” a measuring tool allows you to be. Example: Which is more precise? 19 grams or 18.895 grams
  10. 10. The Dartboard Model Accuracy = Precision = Accuracy = Precision = Accuracy = Precision = Low Low Low High High High
  11. 11. C. Error Def – The difference between the experimental value and the accepted value. Experimental Value – The value measured in the lab Accepted Value – The correc t value, based on reliable references or calculations Equation: [Experimental] – [Accepted] = Error
  12. 12. Sample Problem: James weighs a metal cylinder and finds it has a mass of 48.34 grams. If the actual mass of the cylinder is exactly 50.00 grams, what is his error? 48.34 – 50.00 = -1.66 grams
  13. 13. D. Percent Error Def – The absolute value of the error divided by the accepted value, multiplied by 100 - Compares the error to the accepted value , showing how bad the error really is. Equation: % Error = | error | x 100 accepted value
  14. 14. Steve and Martin each order bricks from a lumber yard. Steve orders 500 bricks to build a wall, but the lumber yard only delivers 499. Martin orders 5 bricks, but only recieves 4. Calculate the error and percent error in each order. 499 – 500 = -1 4 – 5 = -1 499 – 500 = -1 4 – 5 = -1 Steve Martin The error in both orders is the same! In which order is it more significant? | -1 | 500 x 100 = | -1 | 5 x 100 = 0.2% 20%
  15. 15. II. Significant Figures in Measurements Significant Figures – All the digits that are known in a measurement, plus one estimated digit How tall is the rectangle on the left according to the ruler shown? cm 1.64 1 2 Between 1.6 & 1.7 Known Digits Estimated Digit
  16. 16. 4.13 *Note: With all measuring tools, you are expected to estimate one digit beyond what you can actually see marked = significant! 4 5 What is the volume of water in the graduated cylinder to the left? mL Between 4.1 & 4.2 Known Digits Estimated Digit
  17. 17. Reporting Measurements in proper Sig Figs - Measurements must be reported with the correct number of significant figures ! - Significant figures describe the precision with which your measuring tool is calibrated . 0.6 cm 0.62 cm 0.628 cm 0 1 0 1 0 1
  18. 18. Rules for Sig Figs (Rules for Zero’s) 1. All nonzero digits ARE significant. 2. Zero’s appearing between nonzero digits ARE significant. 3. Zeros to the left in front of nonzero digits ARE NOT significant. (They are just placeholders !) 546 = ________ sig figs 13.456 = _________ sig figs 104.3 = ________ sig figs 20.05 = _________ sig figs 0.00224 = ________ sig figs 0.34 = _________ sig figs 3 5 4 4 3 2
  19. 19. Rules for Sig Figs (Rules for Zero’s) 4. Zeros at the end of a number and to the right of a decimal ARE ALWAYS significant. 5. Zeros at the end of a number and LEFT of a decimal are SOMETIMES significant. Unless it is stated that they are specifically measured, we WILL NOT count them as significant. 55.00 = ________ sig figs 320.0 = _________ sig figs 120 = ________ sig figs 33,000 = _________ sig figs 2 2 4 4
  20. 20. V. Significant Figures in Calculations General Rule : Your answer cannot be more precise than the measurements used to calculate that answer. * You must round your answers to the proper number of significant figures. Example: Tennis Ball Drop Times – Averaged Trial 1 - 0.89 seconds Trial 2 - 0.91 seconds Trial 3 - 1.04 seconds Trial 4 - 0.84 seconds Trial 5 - 0.73 seconds Average Time - 0.882 seconds 0.88 seconds
  21. 21. 1. Rounding – Calculations must be rounded to make them consistent with the measurements from which they were calculated. How to Round Numbers: a. First, decide how many significant figures your answer should have. * Follow the rules for addition/subtraction or multiplication/division below! b. Once significant figures have been decided, count that many places , starting from the left .
  22. 22. c. Identify the digit immediately to the right of the last significant figure: <ul><li>If it is less than 5 it is dropped . </li></ul><ul><li>If it is 5 or greater, you must round up the last sig fig . </li></ul><ul><li>Examples: Round the following to 3 sig figs. </li></ul><ul><li>13.542 = _________ </li></ul><ul><li>0.25252 = _________ </li></ul><ul><li>0.0002398 = _________ </li></ul><ul><li>12,346 = _________ </li></ul>13.5 0.253 0.000240 12,300 2.40 x 10 -4 1.23 x 10 4
  23. 23. 2. Addition and Subtraction Rule: The answer should be rounded to have the same number of places after the decimal as the measurement with the LEAST number of decimal places. 24.312 0.2332 19.5 0.4 + 4.66 + 0.66257 19.5 2.6 - 4.66 - 1.55 48.472 1.29577 14.84 1.05 48.5 14.8 1.3 1.1
  24. 24. 3. Multiplication and Division Rule: Round your answer to have the same number of significant figures as the measurement with the least number of significant figures. 24.312 0.2332 19.5 0.40 x 0.66 x 0.66257 19.5 2.6 ÷ 4.6 ÷ 1.55 312.89544 0.06180453 4.2456… 1.6774… 4.2 310 0.062 1.7
  25. 25. VI. International System of Units - Abbreviated SI , after the French name, Le Syst é me International d’Unit é s - A revised version of the Metric System . 1. The Metric System - All metric units are based on the number 10 or multiples of 10 . - Measurements consist of a base unit to which a prefix may be added to make it larger or smaller by a power of 10 .
  26. 26. 3 main base units: a. Length = meter (m) b. Volume = liter (L) c. Mass = gram (g)
  27. 27. Metric Prefixes: ( Memorize!) giga- G 1,000,000,000x larger 10 9 mega- M 1,000,000x larger 10 6 kilo- k 1,000x larger 10 3 hecto- h 100x larger 10 2 deka- da 10x larger 10 1 deci- d 10x smaller (1/10 th or 0.1) 10 -1 centi- c 100x smaller (1/100 th or 0.01) 10 -2 milli- m 1000x smaller (1/1000 th or 0.001) 10 -3 micro-  1,000,000x smaller (1/1,000,000 th or 0.000 001) 10 -6 nano- n 1,000,000,000x smaller (1/1,000,000,000 th or 0.000 000 001) 10 -9 pico- p 1,000,000,000,000x smaller (1/1,000,000,000,000 th or 0.000 000 000 001) 10 -12 Power of 10 Value Symbol Prefix
  28. 28. Examples: 1 kilogram = 10 3 grams (1000x larger) 1 millimeter = 10 -3 meter (1000x smaller) 1 hectoliter = 10 2 liters (100x larger) 10 1 m = 1 dekameter = 1 dam 1 m 10 meters
  29. 29. 10 birds = 1 meter Each bird = 1/10 th of a meter (10 -1 m) 1 bird = 1 decimeter (1 dm) Example: 1 meter stick
  30. 30. 2. Measurements A. Length – measure of linear distance - Unit = meters (m) Associations: 1 meter  1 yard (39.5 inches) 1 inch = 2.54 centimeters 1 mile = 1.6 kilometers 1 kilometer = 0.6 miles ( 10 km = 6 mi )
  31. 31. B. Volume – the amount of space an object takes up <ul><li>Units = cubic meters (m 3 ) </li></ul><ul><ul><ul><li>liters (L) </li></ul></ul></ul>SI Unit Non-SI Unit
  32. 32. Ways to Measure Volume 1. Geometric Solid – (cube, rectangular solid, pyramid, cylinder, sphere, etc…) - use an equation to derive the volume from length measurements Example 1: Rectangular Solid volume = length x width x height volume = meters x meters x meters = m 3 volume = cm x cm x cm = cm 3 Kleenex Box = 22 cm x 11 cm x 5 cm = 1210 cm 3
  33. 33. Example 2: Cylindrical Solid (area of base x height) area of circle =  r 2 volume =  r 2 h * r = radius (1/2 the diameter) Petri Dish diameter = 9.5 cm radius = 4.75cm height = 2.0 cm volume = 141.8 cm 3
  34. 34. 2. Liquids – pour the liquid into a measured container (graduated cylinder) - read the level of the meniscus in liters or mL Note: Liquids are usually measured in liters or mL , while solids are usually measured in m 3 or cm 3 . Associations: 1 liter  1 quart (4 cups) 1 gallon  4 liters 1 mL  20 drops 1 mL = 1 cm 3 = 1 cm x 1cm x 1 cm 1 L = 1 dm 3 = 10cm x 10cm x 10cm 1 L = 1000 mL
  35. 35. 3. Irregular shaped solids – Water displacement ! - Dunk an object in water and the water level goes up ! 4.13 mL 4.78 mL - Simply subtract the final and initial volumes to get difference – Indirect method! 4 5 4 5 Volume _______ Volume _______
  36. 36. C. Mass – measures the quantity of matter an object contains <ul><li>SI unit – kilogram (kg) – standard! </li></ul><ul><li>Base unit = gram </li></ul>Weight – measures the pull of gravity on a given mass <ul><li>Weight changes with location. (On moon = 1/6 th earth) </li></ul><ul><li>An object can be weightless , but never massless. </li></ul>
  37. 37. 1 kg = mass of 1 L of water at 4 degrees Celsius 1 kg = 2.2 lbs 1 ounce  28 grams 1 kg = 1000 grams 1 penny  3 grams
  38. 38. VII. Temperature Definition – a measure of the average kinetic energy of particles in matter. - Kinetic energy is energy of motion , therefore, temperature actually measures the speed of particles . Wikipedia.org – Temperature (click here)
  39. 39. - Temperature also describes the direction of heat flow – from hotter to colder a. When you hold an ice cube it feels cold = heat flowing from hand to ice b. When you hold an cup of coffee it feels hot = heat flowing from coffee to hand
  40. 40. Temperature Scales: a. Celsius scale – based on the boiling and freezing points of water b. Kelvin scale – based on absolute zero , the lowest temperature theoretically possible. * At absolute zero, all particle motion stops !
  41. 41. Fahrenheit =  F Celsius =  C Kelvin = K -273 0 100 -460 32 212 373 273 0 Freezing point of water Boiling point of water Absolute Zero
  42. 42. The End
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