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Unit 2. Measurement

Unit 2. Measurement. Do Now. In your own words, what do you think is the difference between: Accuracy and Precision?. A. Accuracy vs. Precision. Accuracy - how close a measurement is to the accepted value Precision - how close a series of measurements are to each other.

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Unit 2. Measurement

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  1. Unit 2. Measurement

  2. Do Now • In your own words, what do you think is the difference between: • Accuracy and Precision?

  3. A. Accuracy vs. Precision • Accuracy - how close a measurement is to the accepted value • Precision - how close a series of measurements are to each other ACCURATE = CORRECT PRECISE = CONSISTENT

  4. ACCURATE = CORRECTPRECISE = CONSISTENT

  5. your value accepted value B. Percent Error • Indicates accuracy of a measurement

  6. % error = 2.90 % B. Percent Error • A student determines the density of a substance to be 1.40 g/mL. Find the % error if the accepted value of the density is 1.36 g/mL.

  7. C. Significant Figures • Indicate precision of a measurement. • Recording Sig Figs • Sig figs in a measurement include the known digits plus a final estimated digit

  8. C. Significant Figures • Indicate precision of a measurement. • Recording Sig Figs • Sig figs in a measurement include the known digits plus a final estimated digit 2.35 cm

  9. C. Significant Figures • Counting Sig Figs (Table 2-5, p.47) • Count all numbers EXCEPT: • Leading zeros -- 0.0025 (not significant) • Trailing zeroswithout a decimal point -- 2,500 (not Significant) • Zeros between numbers are significant

  10. C. Significant Figures Counting Sig Fig Examples 1. 23.50 1. 23.50 2. 402 2. 402 3. 5,280 3. 5,280 4. 0.080 4. 0.080

  11. C. Significant Figures Counting Sig Fig Examples 1. 23.50 1. 23.50 4 sig figs 3 sig figs 2. 402 2. 402 3. 5,280 3. 5,280 3 sig figs 2 sig figs 4. 0.080 4. 0.080

  12. C. Significant Figures • Calculating with Sig Figs • Multiply/Divide – The # with the fewest sig figs determines the # of sig figs in the answer.

  13. Multiplication and Division Rules • Do the sum • Round the answer to the least significant figure in the problem • 13.91g/cm3)(23.3cm3) = 324.103g 4SF3SF3SF 324g

  14. C. Significant Figures • Calculating with Sig Figs (con’t) • Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer.

  15. Addition and Subtraction Rules • Stack the numbers so that the decimal point is aligned • Do the sum • Figure out which number has least decimal place (least precise/decimal area least far out) • Draw a line after the last number with the least decimal place • Round the digit by looking at the number that follows

  16. Example 3.75 mL+ 4.1 mL 7.85 mL  7.9 mL

  17. C. Significant Figures • Calculating with Sig Figs (con’t) • Exact Numbers do not limit the # of sig figs in the answer. • Counting numbers: 12 students • Exact conversions: 1 m = 100 cm • “1” in any conversion: 1 in = 2.54 cm

  18. 5. (15.30 g) ÷ (6.4 mL)  2.4 g/mL 2 SF Practice Problems 4 SF 2 SF = 2.390625 g/mL 6. 18.9 g - 0.84 g  18.1 g 18.06 g

  19. D. Scientific Notation 65,000 kg  6.5 × 104 kg • Converting into Sci. Notation: • Move decimal until there’s 1 digit to its left. Places moved = exponent. • Large # (>1)  positive exponentSmall # (<1)  negative exponent • Only include sig figs.

  20. 7. 2,400,000 g 8. 0.00256 kg 9. 7  10-5 km 10. 6.2  104 mm D. Scientific Notation Practice Problems

  21. 7. 2,400,000 g 8. 0.00256 kg 9. 7  10-5 km 10. 6.2  104 mm D. Scientific Notation Practice Problems 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

  22. EXE EXP EXP ENTER EE EE D. Scientific Notation • Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104mol) = Type on your calculator: 5.44 7 8.1 4 ÷ = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

  23. y y x x E. Proportions • Direct Proportion • Inverse Proportion

  24. Units of Measurement

  25. A. Number vs. Quantity • Quantity - number + unit UNITS MATTER!!

  26. B. SI Units Quantity Symbol Base Unit Abbrev. Length l meter m Mass m kilogram kg Time t second s Temp T kelvin K Amount n mole mol

  27. mega- kilo- k M 106 103 BASE UNIT deci- --- d 100 10-1 centi- c 10-2 milli- m 10-3 micro-  10-6 nano- n 10-9 pico- p 10-12 B. SI Units Prefix Symbol Factor

  28. M V D = C. Derived Units • Combination of base units. • Volume (m3 or cm3) • length  length  length 1 cm3 = 1 mL 1 dm3 = 1 L • Density • (kg/m3 or g/mL or g/cm3) • mass per volume

  29. D. Density Mass (g) Volume (cm3)

  30. Problem-Solving Steps 1. Analyze 2. Plan 3. Compute 4. Evaluate

  31. D. Density • An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? WORK:

  32. D. Density • An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass. GIVEN: V = 825 cm3 D = 13.6 g/cm3 M = ? WORK: M = DV M = (13.6 g/cm3)(825cm3) M = 11,200 g

  33. D. Density • A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g WORK:

  34. WORK: V = M D V = 25 g 0.87 g/mL D. Density • A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid? GIVEN: D = 0.87 g/mL V = ? M = 25 g V = 29 mL

  35. III. Unit Conversions

  36. To the left or right? A. SI Prefix Conversions 1. Find the difference between the exponents of the two prefixes. 2. Move the decimal that many places.

  37. kilo- mega- M k 106 103 deci- BASE UNIT d --- 100 10-1 centi- c 10-2 milli- m 10-3 micro-  10-6 nano- n 10-9 pico- p 10-12 A. SI Prefix Conversions Prefix Symbol Factor move left move right

  38. 1) 20 cm = ______________ m 2) 0.032 L = _____________ mL 3) 45 m = ______________ nm 4) 805 dm = ______________ km A. SI Prefix Conversions

  39. 1) 20 cm = ______________ m 2) 0.032 L = ______________ mL 3) 45 m = ______________ nm 4) 805 dm = ______________ km A. SI Prefix Conversions 0.2 32 45,000 0.0805 C. Johannesson

  40. B. Dimensional Analysis • The “Factor-Label” Method • Units, or “labels” are canceled, or “factored” out

  41. B. Dimensional Analysis • Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel. 3. Multiply all top numbers & divide by bottom number. 4. Check units & answer.

  42. B. Dimensional Analysis • Lining up conversion factors: • ARE THESE THE SAME? = 1 1 in = 2.54 cm 2.54 cm 2.54 cm 1 = 1 in = 2.54 cm 1 in 1 in

  43. qt mL  B. Dimensional Analysis • How many milliliters are in 1.00 quart of milk? 1 L 1.057 qt 1000 mL 1 L 1.00 qt = 946 mL

  44. lb cm3 B. Dimensional Analysis • You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3. 1 cm3 19.3 g 1 kg 2.2 lb 1000 g 1 kg 1.5 lb = 35 cm3

  45. in3 L B. Dimensional Analysis • How many liters of water would fill a container that measures 75.0 in3? 1 L 1000 cm3 (2.54 cm)3 (1 in)3 75.0 in3 = 1.23 L

  46. cm in B. Dimensional Analysis 5) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off? 8.0 cm 1 in 2.54 cm = 3.2 in

  47. cm yd B. Dimensional Analysis 6) Taft football needs 550 cm for a 1st down. How many yards is this? 1 ft 12 in 1 yd 3 ft 1 in 2.54 cm 550 cm = 6.0 yd

  48. cm pieces B. Dimensional Analysis 7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? 1 piece 1.5 cm 100 cm 1 m 1.3 m = 86 pieces

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