1. Chapter 3 Scientific Measurement
Hingham High School
Mr. Clune
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2. Measurements Qualitative measurements - words
Quantitative measurements – involves numbers (quantities)
Depends on reliability of instrument
Depends on care with which it is read
Scientific Notation
Coefficient raised to power of 10

3. Scientific Notation
Multiplication
Multiply the coefficients, add the exponents
4 + 7 = 11
(2 X 104) X (3 X 107)
2 X 3 = 6
6 X 1011

4. 2 X 104 8 X 109 9 - 5 = 4 4 X 105 8 4 = 2 Scientific Notation Division
Divide the coefficients, subtract the denominator exponent from numerator exponent
8 X 109
4 X 105
9 - 5 = 4 8 4
= 2
2 X 104

5. Scientific Notation
Before adding or subtracting in scientific notation, the exponents must be the same
Calculators will take care of this

6. Scientific Notation
Addition
Line up decimal; add as usual the coefficients; exponent stays the same
(25 X 104) + (3.0 X 106)
(25 X 104) + (300. X 104)
(325 X 104)

7. Scientific Notation
Subtraction
Line up decimal; subtract coefficients as usual; exponent remains the same
(25 X 104) - (150. X 103)
(25 X 104) - (15.0 X 104)
(10 X 104)

8. Measurements and Their Uncertainty
Need to make reliable measurements in the lab
Accuracy – how close a measurement is to the true value
Precision – how close the measurements are to each other (reproducibility)

9. Bad Accuracy
And
Good Precision

10. Bad Accuracy
And
Bad Precision

11. Good Accuracy
And
Bad Precision

12. Good Accuracy
And
Good Precision

13. Measurements and Their Uncertainty
Accepted value – correct value based on reliable references
Experimental value – the value measured in the lab
Error – the difference between the accepted and experimental values

14. Measurements and Their Uncertainty
Error = accepted – experimental
Can be positive or negative
Percent error = the absolute value of the error divided by the accepted value, times 100%
| error |
accepted value
% error =
x 100%

15. % Error = 2% % Error Example Accepted Value = 100g
Experimental Value = 102g
% Error =
| Acc – Exp | Acc
X 100%
% Error =
| 100 – 102 | 100
X 100%
% Error = 2%

16. Significant Figures
Significant figures in a measurement include all of the digits that are known, plus a last digit that is estimated.
Note Fig. 3.4, page 66
Rules for counting sig. figs.?
Zeroes are the problem
East Coast / West Coast method

17. 2. Zeros between nonzero digits 10003 mL (5) 0.2005 ms (4)
Significant Figures
1. All nonzero digits
457 cm (3)
0.35 g (2)
2. Zeros between nonzero digits
10003 mL (5)
ms (4)

18. 3. Zeros to the left of the first nonzero digits in a number are
Significant Figures
3. Zeros to the left of the first
nonzero digits in a number are
not significant; they merely
indicate the position of the
decimal point.
0.02 g (1)
cm (2)

19. 4. When a number ends in zeros that are to the right of the decimal
Significant Figures
4. When a number ends in zeros that
are to the right of the decimal
point, they are significant.
g (3)
3.0 cm (2)

20. 5. When a number ends in zeros that are not to the right of a decimal
Significant Figures
5. When a number ends in zeros that
are not to the right of a decimal
point, the zeros are not necessarily
significant.
130 cm (2)
10,300 g (3)

21. Counting Significant Fig.
Sample 3-1, page 69
Rounding
Decide how many sig. figs. Needed
Round, counting from the left
Less than 5? Drop it.
5 or greater? Increase by 1
Sample 3-2, page 70

22. Sig. fig. calculations Addition and Subtraction
The answer should be rounded to the same number of decimal places as the least number in the problem
Sample 3-3, page 60

23. { 26.46 + 4.123 30.583 Sig. fig. calculations
this has the least digits to the right of the decimal point (2)
26.46
 30.583    
Rounds off to

24. Sig. Fig. calculations Multiplication and Division
Round the answer to the same number of significant figures as the least number in the measurement
Sample 3-4, page 61

25. { 2.61 x1.2 3.132 Sig. Fig. calculations
this has the smaller number of significant figures (2)
2.61 x1.2    3.132     
Rounds off to 3.1

26. International System of Units
The number is only part of the answer; it also need UNITS
Depends upon units that serve as a reference standard
The standards of measurement used in science are those of the Metric System

27. International System of Units
Metric system is now revised as the International System of Units (SI), as of 1960
Simplicity and based on 10 or multiples of 10
7 base units
Table 3.1, page 63

28. International System of Units
Sometimes, non-SI units are used
Liter, Celsius, calorie
Some are derived units
Made by joining other units
Speed (miles/hour)
Density (grams/mL)

29. Common prefixes Kilo (k) = 1000 (one thousand)
Deci (d) = 1/10 (one tenth)
Centi (c) = 1/100 (one hundredth)
Milli (m) = 1/1000 (one thousandth)
Micro () = (one millionth)
Nano (n) = (one billionth)

30. Length In SI, the basic unit of length is the meter (m)
Length is the distance between two objects – measured with ruler
We make use of prefixes for units larger or smaller

31. Volume The space occupied by any sample of matter
Calculated for a solid by multiplying the length x width x height
SI unit = cubic meter (m3)
Everyday unit = Liter (L), which is non-SI

32. Volume Measuring Instruments
Graduated cylinders
Pipet
Buret
Volumetric Flask
Syringe

33. Volume changes?
Volume of any solid, liquid, or gas will change with temperature
Much more prominent for GASES
Therefore, measuring instruments are calibrated for a specific temperature, usually 20 oC, which is about normal room temperature

34. Volume – (m3)

35. Volume (L)
1dm3=1L

36. Volume

37. Volume (mL)
1cm3=1mL
1cm

38. Volume – Liter (L)
1L=1.05qt

39. Units of Mass Mass is a measure of the quantity of matter
Weight is a force that measures the pull by gravity- it changes with location
Mass is constant, regardless of location

40. Mass – KiloGram (kg)
1kg=2.2lbs

41. Working with Mass
The SI unit of mass is the kilogram (kg), even though a more convenient unit is the gram
Measuring instrument is the balance scale

42. Temperature Kelvin (K) Based on Absolute Zero Celsius (°C)
Water freezes at 0°C (273K)
Water boils at 100°C (373K)

43. Temperature
Water freezes at 0°C (273K)
Water boils at 100°C (373K)

44. BP of H2O
FP of H2O
Temperature (°C, K)
Absolute Zero

45. °C = K - 273 345K = ? °C °C = 345K – 273 72°C Temperature
Convert Kelvin to Celsius
°C = K - 273
345K = ? °C
°C = 345K – 273
72°C

46. K = °C + 273 20 °C = ? K K= 20°C – 273 293K Temperature
Convert Celsius to Kelvin
K = °C + 273
20 °C = ? K
K= 20°C – 273
293K

47. Time – Seconds (s)

48. The capacity to do work or produce heat
Energy
The capacity to do work or produce heat
Joule (J)
Calorie (Cal)
Energy needed to raise 1g of 1 °C

49. Homework
Practice Problem 16
Page 78
Section Assessment
Questions: 18-27(odd)
Page 79
Due: 10/7/04

50. Dimensional Analysis
Converting Units

51. Conversion Problems
50cm = ?m
100cm = 1m 1m
100cm
100cm 1m

52. Conversion Problems 1m
100cm
50cm X =
0.50 m

53. Conversion Problems
0.045kg =? g
1000g = 1kg
1kg
1000g
1000g
1kg

54. Conversion Problems
1000g
1kg
0.045kg X =
45g

55. Conversion Problems
2.5hr =? s
60min = 1hr
1hr
60min
60min
1hr

56. Conversion Problems
2.5hr =? s
60s = 1min
1min
60s
60s
1min

57. Conversion Problems
60s
min
60min
1hr
2.5hr X X =
9000s

58. Homework
Practice Problem 35-37
Pages
Due: 10/7/04

59. Density Which is heavier- lead or feathers?
It depends upon the amount of the material
A truckload of feathers is heavier than a small pellet of lead
The relationship here is between mass and volume- called Density

60. The formula for density is: mass volume
Common units are g/mL, or possibly g/cm3, (or g/L for gas)
Density is a physical property, and does not depend upon sample size
Density =

61. Things related to density
What happens when corn oil and water are mixed?
Why?
Will lead float?

62. Density and Temperature
What happens to density as the temperature increases?
Mass remains the same
Most substances increase in volume as temperature increases
Thus, density generally decreases as the temperature increases

63. Density and water Sample 3-10,11, page 91-92
Water is an important exception
Over certain temperatures, the volume of water increases as the temperature decreases
Does ice float in liquid water?
Why?
Sample 3-10,11, page 91-92

64. Specific Gravity
A comparison of the density of an object to a reference standard (which is usually water) at the same temperature
Water density at 4 oC = 1 g/cm3
1g of H2O = 1mL = 1 g/cm3

65. Formula Note there are no units left, since they cancel each other
D of substance (g/cm3)
D of water (g/cm3)
Note there are no units left, since they cancel each other
Measured with a hydrometer – p.72
Uses? Tests urine, antifreeze, battery
Specific gravity =

66. Temperature Heat moves from warmer object to the cooler object
Glass of iced tea gets colder?
Remember that most substances expand with a temp. increase?
Basis for thermometers

67. Temperature scales Celsius scale- named after a Swedish astronomer
Uses the freezing point(0 oC) and boiling point (100 oC) of water as references
Divided into 100 equal intervals, or degrees Celsius

68. Temperature scales Kelvin scale (or absolute scale)
Named after Lord Kelvin
K = oC + 273
A change of one degree Kelvin is the same as a change of one degree Celsius
No degree sign is used

69. Temperature scales Water freezes at 273 K Water boils at 373 K
0 K is called absolute zero, and equals –273 oC
Fig. 3.19, page 75
Sample 3-6, page 75