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Daily Challenge 9/16

Daily Challenge 9/16. Is there a difference between accuracy and precision? Why or why not?. Accuracy vs. Precision. ACCURACY – HOW CLOSE A MEASUREMENT COMES TO THE TRUE VALUE; “CORRECT?” PRECISION – HOW CLOSE A SERIES OF MEASUREMENTS ARE TO ONE ANOTHER; “Consistent?”. 3.1.

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Daily Challenge 9/16

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  1. Daily Challenge 9/16 • Is there a difference between accuracy and precision? Why or why not?

  2. Accuracy vs. Precision ACCURACY – HOW CLOSE A MEASUREMENT COMES TO THE TRUE VALUE; “CORRECT?” PRECISION – HOW CLOSE A SERIES OF MEASUREMENTS ARE TO ONE ANOTHER; “Consistent?” 3.1

  3. Accuracy vs. Precision NO NO YES YES NO YES 3.1

  4. Determining Error “KNOWLEDGE RESTS NOT UPON TRUTH ALONE, BUT UPON ERROR ALSO” 3.1

  5. ERROR = EXPERIMENTAL VALUE – ACCEPTED VALUE VALUE MEASURED IN THE LAB CORRECT VALUE Determining Error 3.1

  6. PERCENT ERROR = Determining Error ABSOLUTE VALUE!! 3.1

  7. Determining Error • Guess my weight… • Observed????? • Accepted/Correct Value- See drivers license

  8. 1 Determining Error THE ACCEPTED VALUE FOR THE MELTING POINT OF SODIUM CHLORIDE IS 801°C. A STUDENT EXPERIMENTALLY DETERMINED THE MELTING POINT TO BE 702°C. DETERMINE THE ERROR AND THE PERCENT ERROR. A ERROR = EXPERIMENTAL VALUE – ACCEPTED VALUE – ERROR = 702°C 801°C ERROR = – 99°C 3.1

  9. 1 Determining Error THE ACCEPTED VALUE FOR THE MELTING POINT OF SODIUM CHLORIDE IS 801°C. A STUDENT EXPERIMENTALLY DETERMINED THE MELTING POINT TO BE 702°C. DETERMINE THE ERROR AND THE PERCENT ERROR. A PERCENT ERROR = PERCENT ERROR = 3.1

  10. Significant Figures • IN A MEASUREMENT, ALL OF THE DIGITS THAT ARE KNOWN, PLUS A LAST DIGIT THAT IS ESTIMATED. • THE ESTIMATED DIGIT IS ALWAYS ONE PLACE HOLDER SMALLER THAN THE MARKED INTERVAL IN THE INSTRUMENT. 3.1

  11. Measuring with Significant Figures Determine the position of the marked (“smallest”) interval on the measuring device. What position can you read? 1 1 2 3 4 5 6 7 8 Hundredths ● Hundreds Thousandths Thousands Tens Tenths Ten Thousandths Ones

  12. Measuring with Significant Figures Determine the estimated position . The estimated position is ALWAYS one position to the RIGHT of the marked interval. For example: If the marked interval is the hundreds place, the estimated position is the tens place. 2 1 2 3 4 ● Hundreds Thousands Tens Ones

  13. Measuring with Significant Figures Write the measurement to accurately reflect the marked interval, estimated position and unit. 3 3.4 m 3.4

  14. cm 100 200 300 400 Significant Figures IN A MEASUREMENT, ALL OF THE DIGITS THAT ARE KNOWN, PLUS A LAST DIGIT THAT IS ESTIMATED. THE ESTIMATED DIGIT IS ALWAYS ONE PLACE HOLDER SMALLER THAN THE MARKED INTERVAL IN THE INSTRUMENT. 2 HUNDREDS MARKED POSITION: _____________________ TENS ESTIMATED POSITION: _____________________ MEASUREMENT: _____________________ 370 cm 3.1

  15. cm 1 2 3 4 Significant Figures IN A MEASUREMENT, ALL OF THE DIGITS THAT ARE KNOWN, PLUS A LAST DIGIT THAT IS ESTIMATED. THE ESTIMATED DIGIT IS ALWAYS ONE PLACE HOLDER SMALLER THAN THE MARKED INTERVAL IN THE INSTRUMENT. 3 ONES MARKED POSITION: _____________________ TENTHS ESTIMATED POSITION: _____________________ MEASUREMENT: _____________________ 2.5 cm 3.1

  16. 0.1 0.2 0.3 0.5 0.4 cm Significant Figures IN A MEASUREMENT, ALL OF THE DIGITS THAT ARE KNOWN, PLUS A LAST DIGIT THAT IS ESTIMATED. THE ESTIMATED DIGIT IS ALWAYS ONE PLACE HOLDER SMALLER THAN THE MARKED INTERVAL IN THE INSTRUMENT. 4 HUNDREDTHS MARKED POSITION: _____________________ THOUSANDTHS ESTIMATED POSITION: _____________________ MEASUREMENT: _____________________ 0.270 cm 3.1

  17. 200 100 Significant Figures 5 300 200 100 mL TENS MARKED POSITION: _____________________ ONES ESTIMATED POSITION: _____________________ MEASUREMENT: _____________________ 163 mL 3.1

  18. Daily Challenge 9/16 • Explain the correct way to obtain a measurement with correct significant figures.

  19. Two kinds of numbers: • Exact numbers • Infinite number of significant figures. • Example: There are exactly 12 eggs in a dozen. • Example: There are exactly 1000 m in 1 km. • Inexact numbers (any measurement) • Depends on the precision of the instrument. • Example: If I quickly measure the width of a piece of notebook paper, I might get 220 mm (2 significant figures). If I am more precise, I might get 216 mm (3 significant figures). An even more precise measurement would be 215.6 mm (4 significant figures).

  20. 1 2 Significant Figures Rules ALL NONZERO DIGITS ARE SIGNIFICANT • 12.5 L HAS 3 SIG. FIGS • 1.254 g HAS 4 SIG. FIGS • ZEROS BETWEEN NONZERO DIGITS ARE SIGNIFICANT • 505 L HAS 3 SIG. FIGS • 4002g HAS 4 SIG. FIGS 3.1

  21. 3 4 Significant Figures Rules ZEROS THAT APPEAR IN FRONT OF NONZERO DIGITS ARE NOT SIGNIFICANT • 0.0045 L HAS 2 SIG. FIGS • 0.101 g HAS 3 SIG. FIGS • ZEROS AT THE END OF A NUMBER & TO THE RIGHT OF THE DECIMAL POINT ARE SIGNIFICANT • 1.010 L HAS 4 SIG. FIGS • 4.0g HAS 2 SIG. FIGS 3.1

  22. 5 Significant Figures Rules • ZEROS AT THE END OF A NUMBER & TO THE LEFT OF THE DECIMAL POINT ARE SIGNIFICANT IF THE DECIMAL IS WRITTEN • 1000 L HAS 1 SIG. FIG • 1000.g HAS 4 SIG. FIGS 3.1

  23. 6 Significant Figures Rules • DEFINED QUANTITIES AND EXACT (NOT MEASURED) NUMBERS HAVE INFINITE SIG FIGS. • π HAS INFINITE SIG. FIGS • 1 DOZEN HAS INFINITE SIG. FIGS 3.1

  24. Significant Figures Practice DETERMINE HOW MANY SIG FIGS ARE IN THE FOLLOWING NUMBERS 6 3 (2) 6 (2) • 808 mL ________ b. 9584.02 g ________ • c. 124500. cm________ d. 0.01375 L ________ • e. 505.0 m ________ f. 1.00 cm3 ________ • g. 967 g ________ h. 54,000 g ________ • i. 0.08720 g ________ j. 1 mile = 5280 ft ________ 6 (5) 4 (3) 4 (2,4) 3 (4) 3 (1) 2 (5) 4 (4) inf (6) 3.1

  25. Daily Challenge 9/20 • Identify how many significant figures are in the following and then round each number to 3 sig figs. 14,501 12.00 0.08976 14010

  26. Sig Figs in Calculations • ADDITION OR SUBTRACTION • The answer can have no more digits to the right of the decimal point than there are in the measurement with the smallest number of digits to the right of the decimal point. 3.95 cm 2.879 cm + 213.6cm 7 220.429 cm 220.4 cm 3.1

  27. Sig Figs in Calculations • ADDITION OR SUBTRACTION • The answer can have no more digits to the right of the decimal point than there are in the measurement with the smallest number of digits to the right of the decimal point. 14.01 m 2.879 m - 0.0075 m 7 11.124 m 11.12 m 3.1

  28. Sig Figs in Calculations Calculation Calculator says: Answer 10.24 m 3.24 m + 7.0 m 10.2 m 100.0 g - 23.73 g 76.3 g 76.27 g 0.02 cm + 2.371 cm 2.39 cm 2.391 cm 713.1 L - 3.872 L 709.228 L 709.2 L 3.1

  29. 7 Sig Figs in Calculations • MULTIPLICATION OR DIVISION • The answer can have no more significant figures than there are in the measurement with the smallest number of significant figures. 4.05 cm × 0.0059 cm × 500.0 cm = 11.948 cm3 (2) (3) (2) (4) 11.948 cm3→ 12 cm3 3.1

  30. 7 Sig Figs in Calculations • MULTIPLICATION OR DIVISION • The answer can have no more significant figures than there are in the measurement with the smallest number of significant figures. 12.51 mL ÷ 1000 = 0.01251 mL (4) (1) (1) 0.01251 mL → 0.01 mL 3.1

  31. Sig Figs in Calculations Calculation Calculator says: Answer 43.438 m2 5.87 m × 7.4 m 43 m2 99.74 g ÷ 23.73 4.203 g 4.203118 g 0.02 cm × 2.371 cm 0.2 cm2 0.177122 cm2 710 L ÷ 3.872 183.367 L 180 L 3.1

  32. Daily Challenge 9/21 • Calculate the following and record your answer with correct sig figs • 710 L ÷ 3.872 • 0.02 cm + 2.371 cm • 2.36 x 102 mm x 1.6 x 104 mm • 100 g - 23.73 g

  33. SCIENTIFIC NOTATION • A GIVEN NUMBER WRITTEN AS A PRODUCT OF TWO NUMBERS: A× 10B A COEFFICIENT BETWEEN 1 AND 10 A POWER OF 10 3.1

  34. 8 A 3 2 1 SCIENTIFIC NOTATION • WRITE THE FOLLOWING NUMBERS IN SCIENTIFIC NOTATION × 10B × 103 6.2 6,200 m + B WHEN DECIMAL MOVES TO THE LEFT 3.1

  35. 8 A 3 6 2 5 1 4 SCIENTIFIC NOTATION • WRITE THE FOLLOWING NUMBERS IN SCIENTIFIC NOTATION × 10B × 106 8.542 8,542,000 m + B WHEN DECIMAL MOVES TO THE LEFT 3.1

  36. 8 A 1 2 3 SCIENTIFIC NOTATION • WRITE THE FOLLOWING NUMBERS IN SCIENTIFIC NOTATION × 10B × 10-3 2.548 0.002548 m - B WHEN DECIMAL MOVES TO THE RIGHT 3.1

  37. 8 A 1 2 3 SCIENTIFIC NOTATION • WRITE THE FOLLOWING NUMBERS IN SCIENTIFIC NOTATION × 10B × 10-3 1.58 0.00158 m - B WHEN DECIMAL MOVES TO THE RIGHT 3.1

  38. 9 1 3 2 1 SCIENTIFIC NOTATION • WRITE THE FOLLOWING NUMBERS IN STANDARD NOTATION 0.0025 m 2.5 × 10-3 m 64.5 s 6.45 × 101 s 3.1

  39. 9 1 2 2 3 4 1 SCIENTIFIC NOTATION • WRITE THE FOLLOWING NUMBERS IN STANDARD NOTATION 45200 g 4.52 × 104 g 0.0525 mL 5.25 × 10-2 mL 3.1

  40. Daily Challenge 9/23 Calculate the following using correct sig figs. 45.60g ÷ 12.0 20.03 g – 15.42 g 7.89 x 1012 mm x 2.2 x 1017mm

  41. Dimensional Analysis • Problem solving technique • Involves the study of dimensions of physical quantities • Used primarily as a tool for obtaining information about physical systems too complicated for full mathematical solutions

  42. S.U.T.S • S = Starting quantity • Identify only ONE!!!!! • Recognize it because if you change the starting quantity, you change the answer • Think…what do you know you have in the beginning? Or what do you want to convert?

  43. S.U.T.S • U = Unknown Quantity • Identify only ONE!!!!! • Ending quantity • Recognize it because as the units you are looking for • Think…what do you want to find? What units do you want at the end?

  44. S.U.T.S • T = Transformations • RELATIONSHIPS or SET QUANTITIES • Usually everything else in a problem is a relationship!!!!! • Use the form A = B • 1 mol Na = 6.02 x 1023 atoms Na • Think…what can I use to get from starting to unknown?

  45. S.U.T.S • S = Set Up & Solve 10-3 L 1 dL 4.56 mL 1 mL 10-1 L Starting Quantity Transformations

  46. Daily Challenge 9/28 • Round the following numbers to express 3 sig figs. • 2147 m • 20107 mm • 1300.1 cm • 400 L

  47. Daily Challenge 9/25 • Gold has sold for $500.0 per ounce. Considering that there are 16 ounces per pound and 454 grams per pound, how many grams of gold could you buy for one cent? • S:_____________________ • U:_____________________ • T:_____________________ • S:

  48. SUTS Practice • Michael Scott wants to purchase 3 gallons of blue moon custard. Unfortunately, the custard stand only sells custard by the pints. Determine how many pints Michael would need given the following equalities • 1 gallon = 4 quarts, 1 tablespoon = 0.0625 cups, 1 quart = 2 pints

  49. INTERNATIONAL SYSTEM OF UNITS • 1960 INTERNATIONALLY ACCEPTED UNITS FOR MEASUREMENT Quantity Unit Symbol Length meter m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K Amount of substance mol mol 3.2

  50. INTERNATIONAL SYSTEM OF UNITS • Why do we use SI measurements??? • Clearly communicate to one another without having to constantly convert between systems • Every major nation, with the exception of U.S. have adopted the metric system • This system is based on the units of ten

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