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# Scientific Measurements

Scientific Measurements. Accuracy vs. Precision Significant Figures Scientific Notation SI Metric units Density Dimensional Analysis. How good are the measurements?. Scientists use two word to describe how good the measurements are

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## Scientific Measurements

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1. Scientific Measurements Accuracy vs. Precision Significant Figures Scientific Notation SI Metric units Density Dimensional Analysis

2. How good are the measurements? • Scientists use two word to describe how good the measurements are • Accuracy- how close the measurement is to the actual value • Precision- how well can the measurement be repeated

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

4. Differences • Accuracy can be true of an individual measurement or the average of several • Precision requires several measurements before anything can be said about it • examples

5. Let’s use a golf anaolgy

6. Accurate? No Precise? Yes

7. Accurate? Yes Precise? Yes

8. Precise? No Accurate? Maybe?

9. Accurate? Yes Precise? We cant say!

10. In terms of measurement • A room is exactly 10.3 m wide • Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. • Were they precise? • Were they accurate?

11. Accurate and Precise as it relates to Blood Pressure • lets say a person’s blood pressure is truly 124/78. • 3 different people measure it and they get the following data • 110/62 • 110/60 • 112/62 • Is this data accurate or precise, both or neither?

12. Accurate and Precise as it relates to Blood Pressure • lets say a person’s blood pressure is truly 124/78. • 3 different people measure it and they get the following data • 124/58 • 146/90 • 98/64 • Is this data accurate or precise, both or neither?

13. Accurate and Precise as it relates to Blood Pressure • lets say a person’s blood pressure is truly 124/78. • 3 different people measure it and they get the following data • 126/78 • 126/80 • 124/76 • Is this data accurate or precise, both or neither?

14. Types of measurement • Quantitative- use numbers • Qualitative- use description • 4 feet • extra large • Hot • 100ºF

15. Scientists prefer • Quantitative- easy check • Easy to agree upon, no personal bias • The measuring instruments limit how good a measurement can be

16. Significant Figures • Indicate precision of a measurement. • Recording Sig Figs • Sig figs in a measurement include the known digits plus a final estimated digit 2.75 cm

17. Significant Figurescount any # 1-9 • Zeros are tricky 00000000 • Count all numbers EXCEPT: • Never count Leading zeros -- 0.00471 (? sig figs) • Count all trapped zeros 12.07 (? sig figs) • Don’t count Ending zeros unless they have a decimal point -- 7,400 (? sig figs) • Count zeros that have a decimal point at the end 3500.

18. Significant Figures Counting Sig Fig Examples 1. 32.30 2. 4002 3. 3,470 4. 0.090

19. 3 SF Significant Figures • Calculating with Sig Figs • Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (14.22g/cm3)(21.5cm3) = 305.73g 4 SF 3 SF 306g

20. 3 SF Significant Figures • Calculating with Sig Figs • Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. (17.8g/cm3)(11.53cm3) = 205.234g 3 SF 4 SF 205g

21. Significant Figures • Calculating with Sig Figs • Add/Subtract- The # with the lowest decimal value determines the place of the last sig fig in the answer. 224 g + 130 g 354 g 224 g + 130 g 354 g 3.75 mL + 4.1 mL 7.85 mL 3.75 mL + 4.1 mL 7.85 mL  350 g  7.8 mL

22. Significant Figures • Calculating with Sig Figs • Exact Conversions do not limit the # of sig figs in the answer. • Exact conversions: 1 m = 100 cm • 1 in = 2.54 cm • 3 feet = 1 yard

23. (15.30 g) ÷ (6.4 mL)  2.4 g/mL 2 SF Significant Figures Practice Problems 4 SF 2 SF = 2.390625 g/mL

24. Significant Figures Practice Problems 18.9 g - 0.84 g  18.1 g 18.06 g

25. Scientific Notation • Converting into Sci. Notation: • Move decimal until there’s 1 digit to its left. Places moved = exponent. (a # 1-10) • Large # (>1)  positive exponentSmall # (<1)  negative exponent • Only include sig figs. 65,000 kg  6.5 × 104 kg

26. 7. 2,400,000 g 8. 0.00256 kg 9. 7  10-5 km 10. 6.2  104 mm Scientific Notation Practice Problems

27. 7. 2,400,000 g 8. 0.00256 kg 9. 7  10-5 km 10. 6.2  104 mm Scientific Notation Practice Problems 2.4  106 g 2.56  10-3 kg 0.00007 km 62,000 mm

28. 2nd 2nd ENTER EE EE Scientific Notation • Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your TI-30 x IIS calculator: 5.44 7 8.1 4 ÷ = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

29. n n x10 x10 Scientific Notation • Calculating with Sci. Notation (5.44 × 107 g) ÷ (8.1 × 104 mol) = Type on your TI-30XS Multiview calculator: 5.44 (8.1 4 7 ENTER ÷ enter = 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

30. 0ºC Measuring Temperature

31. 0ºC Measuring Temperature • Celsius scale. • water freezes at 0ºC • water boils at 100ºC • body temperature 37ºC • room temperature 20 - 25ºC

32. Convert Celsius to Fahrenheit 9/5 C + 32 = F Ex. Convert 10 C to F (9/5 x 10) + 32 = 50 F

33. Convert Fahrenheit to Celsius 5/9 (F – 32) = C Ex. Convert 45 F to C 5/9 (45 – 32) = 7.2 C

34. 273 K Measuring Temperature • C + 273 = K • K -273 = C Convert 25 C into K 25 C + 273 = 298 K Convert 303 K into C 303 K – 273 = 30 C

35. 273 K Measuring Temperature • Kelvin starts at absolute zero (-273 º C) • degrees are the same size • C = K -273 • K = C + 273 • Water freezes at 273 K • Water boils at 373 K • Kelvin is always bigger. • Kelvin can never be negative.

36. Quantity Base Unit Symbol • Length – meter m • Mass - gram g • Time – second s • Temperature - Kelvin or ºCelsius K or C • Energy - JoulesJ • Volume - LiterL • Amount of substance - molemol

37. Quantity Base Unit Symbol • Length – meter m • Mass - gram g • Time – second s • Temperature - Kelvin or ºCelsius K or C • Energy - Joules J • Volume - Liter L • Amount of substance - mole mol

38. mega- kilo- k M 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 SI Units Prefix Symbol Factor Million 1000 1 1/10 = .1 1/100 = .01 1/1000= .001 .000001

39. SI Units – Standard International 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

40. M V D = Volume and Density • Combination of base units. • Volume (cm3) • length  length  length 1 cm3 = 1 mL • Density = g/cm3 • mass per volume

41. 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 = 11,220 g M= 11,200 g

42. WORK: V = M D V = 25 g =28.736 0.87 g/mL 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

43. k h D d c m Converting • how far you have to move on this chart, tells you how far, and which direction to move the decimal place. • The box is the base unit, meters, Liters, grams, etc.

44. k h D d c m Conversions • Change 5.6 m to millimeters • starts at the base unit and move three to the right. • move the decimal point three to the right 5 6 0 0

45. k h D d c m Conversions • Change 5.6 km to millimeters

46. k h D d c m Conversions • Change 5.6 km to millimeters • Km to mm is 6 steps • 5.6 E6 mm or 5,600,000 mm

47. k h D d c m Conversions • convert 25 mg to grams • convert 0.45 km to mm • convert 35 mL to liters

48. k h D d c m Conversions • convert 25 mg to grams .025 g • convert 0.45 km to mm 450,000 mm • convert 35 mL to liters .035 L