1. Chapter 3 – Scientific Measurement

2. Chapter Preview 3.1 - Importance of Measurement
Qualitative/Quantitative measurements
Scientific Notation
3.2 - Uncertainty in Measurements
Accuracy, precision, & error
SIGFIGS!
3.3 - International System of Units
Length, Volume, Mass
Metric System
3.4 - Density
What is it?
Calculations
3.5 - Temperature
Different scales

3. Section 3.1 The Importance of Measurement
Qualitative measurements – non-numerical measurements
Quantitative measurements – measurements in a definite, numerical form… ALWAYS with units.
If you don’t put a unit on an answer, it’s wrong.

4. Measurements: Qualitative or Quantitative?
3 meters
Large trash cans
5 car lengths
Round
Brown basketballs
6 runs
Several slugs
98 degrees
Millions of stars

5. Scientific Notation
In chemistry and other sciences, very small or large numbers are often used
602,000,000,000,000,000,000,000
Scientific notation is a method of writing these numbers in a shorter, easier form.
6.02 x 1023

6. Scientific Notation Scientific Notation: M x 10n
In scientific notation, a number is written as the product of two numbers: a coefficient and 10 raised to a power.
Scientific Notation: M x 10n
1 ≤ M ≤ 9 and n is a whole number
6.02 x 1023
6.02 is the coefficient
1023 moves the decimal place
The exponent is the number of decimal places moved

7. Scientific notation
The following are examples of where to locate the scientific notation button and on how to type scientific notation in.

15. Examples Write each measurement in scientific notation
665,000

16. Standard Notation 3 x 104 0.056 x 103 4.56 x 10-9
Write the following measurements in standard notation
3 x 104
0.056 x 103
4.56 x 10-9

17. Scientific Notation Multiplying and dividing
To multiply:
Multiply the coefficients to get the new coefficient
Add the exponents to get the new exponent
Ex: (2.0 x 103)(3.0 x 104) = 6.0 x 107
To divide:
Divide the coefficients to get the new coefficient
Subtract the exponents to get the new exponent
Ex: (10.0 x 105)/(5.0 x 102) = 2.0 x 103

18. Adding and subtracting
The decimal places must be in the same spot on the standard notation number
Align the decimal places by shifting the decimal and adjusting the exponent until the exponents are the same
Ex: x x 103  x x 103
Then add or subtract. Keep the exponent
Ex: x 103

19. Examples (6.50 x 104) x (5.0 x 106) (6.50 x 104) x (5.0 x 10-5)

20. A scientific calculator has a scientific notation button on your calculator. It will make solving problems in chemistry much easier!
TI = Normally select the 2nd button followed by the ee button.
Casio = Normally select the exp button.

21. Section 3.2 Uncertainty in Measurements
Objectives:
Distinguish among the accuracy, precision, and error of a measurement
Identify the number of significant figures in a measurement and in the result of a calculation

22. Section 3.2 Uncertainty in Measurements
All measurements have some degree of uncertainty
Meter stick
Making precise measurements reliably is important

25. Uncertainty in Measurements
Correctness and reproducibility in measurements have certain terms.
Accuracy - how close the measurement is to the actual value.
Precision – how consistent a series of measurements is.

26. Uncertainty in Measurements

27. Uncertainty in Measurements
To evaluate the accuracy of a measurement, you observe the accepted value and experimental value
Accepted value – the correct value based on reliable references
Experimental value – the value actually measured in the lab

28. Uncertainty in Measurements
Error – the difference between the accepted and experimental value
Error = experimental value – accepted value
Percent error – shows the error relative to the accepted value

29. Example
You measure the freezing temperature of water to be 2 degrees Celsius. What is the percent error of your measurement? You will need to convert to Kelvin! (Celsius = Kelvin)

30. Activity Lab: Percent Error
Get into groups of two.
Complete each station.

31. Significant Figures
Significant figures include all of the digits that are known, plus a last digit that is estimated.

32. Significant Figures Rules
All nonzero digits are significant.
456 cm
1.982 km
Rule #2
All zeros appearing in between nonzero digits are significant.
2,002.3 mi
100.5 lbs

33. Significant Figures Rules
Leftmost zeros appearing in front of nonzero digits are not significant. m km
Rule #4
Rightmost zeros appearing after a nonzero digit with NO decimal are NOT significant.
200 mi
45,000,000 lbs

34. Significant Figures Rules
Rightmost zeros appearing after a nonzero digit WITH a decimal ARE significant.
32.00 m
120.0 km
Rule #6
There are two situations in which measurements have an unlimited number of significant figures.
Counting items with whole numbers. (i.e. people)
Exactly defined quantities. (60 min = 1 hour)

35. 123 meters 30.0 meters 3 sig figs 3 sig figs 0.123 meter
Examples
123 meters
3 sig figs
0.123 meter
40,506 meters
5 sig figs
x 104 meters
30.0 meters
3 sig figs
22 meter sticks
Unlimited
meter
4 sig figs
98,000 meters
2 sig figs

36. Sig Figs in Calculations
Rounding Sig Figs
An answer cannot be more precise than the least precise measurement from which it was calculated.
To round a number, you must first decide how many significant figures the answer should have. It depends on the given measurements.

37. Rules for Rounding Numbers
If the digit following the last digit to be retained is:
Then the last digit should:
Example (rounded to three significant figures)
Greater than 5
Be increased by 1
42.68 g → 42.7 g
Less than 5
Stay the same
17.32 m → 17.3 m
5, followed by nonzero digit(s)
cm → 2.79 cm
5, not followed by nonzero digit(s), and preceded by an odd digit
4.635 kg → 4.64 kg (because 3 is odd)
5, not followed by nonzero digit(s), and the preceding significant digit is even
78.65 mL → 78.6 mL
(because 6 is even)

38. Examples: Round each measurement to three significant figures.
x 108 m m
9009 m
x 10-3 m m

39. Sig Figs in Calculations
Addition & Subtraction
Add / Subtract Normally
Find the least place value that all given numbers have in common
Round to that least place value.

40. Examples
12.52 m m m
m – m

41. Sig Figs in Calculations
Multiplication & Division
Multiply / Divide Normally
Count the number of sig figs in each given number.
Round to the least amount of sig figs.

42. Examples
7.55 m x 0.34 m
g ÷ 8.4 mL

43. Section 3.3 International System of Units
The International System of Units (SI) is a revised version of the metric system.
Le Systéme International d’Unités
It was adopted by international agreement in 1960.

44. Base Units
There are seven SI base units. From these base units, all other SI units are derived.

45. Derived Units
Derived units are made from a combination of base units. Examples include:
m3 = Volume
g/cm3 = Density
Pa = Pressure

46. Prefixes Used in the Metric System

47. Units of Length 1 km = 1000 m Meter (m) is base unit
1 dm = 1/10 m 1 dm = 0.1 m
1 cm = 1/100 m 1 cm = 0.01 m
1 mm = 1/1000 m 1 mm = m
1 μm= 1/ m 1 μm = m
1 nm = 1/ m 1 nm = m

48. Examples Convert the following lengths: 25 m to cm 1.67 mm to m
2,300 mm to km
4.5 x 109 nm to cm

49. Units of Volume
The space occupied by any sample of matter is called its volume.
Length x width x height = volume
1m x 1m x 1m = 1 m3
Other useful volume units include:
Liter (L)
Milliliter (mL)
Cubic centimeter (cm3)

50. Examples Convert the following volumes: 35 mL to L 2300 m3 to cm3
15 mL to cm3
25 cm3 to mm3

51. Units of Mass Mass is how much matter an object has
Mass base unit – kilogram (kg)
Weight is dependent on gravity
Weight – force on object due to gravity
An astronaut’s weight on the moon is 1/6th of the weight on Earth. His/her mass is the same no matter where they are!

52. Examples Convert the following masses: 0.075 kg to grams 1,200 g to kg
73.5 mg to cg
3.50 x 108 μg to g

53. Section 3.4 Density Density – amount of mass in a given volume
Mass per unit volume
Common Units
g/cm3
kg/m3
g/mL

54. Example
A copper penny has a mass of 3.1 g and a volume of 0.35 cm3. What is the density of copper?

55. Example
The density of silver at 20 ˚C is 10.5 g/cm3. What is the volume of a 68 g bar of silver?

56. Example
Find the mass of an object that has a density of g/cm3 and a volume of 1.0 cm3.

57. Specific Gravity
Specific gravity – is a comparison of the density of a substance with the density of a reference substance, usually at the same temperature.
Usually compared to water
Measured with hydrometer

58. Section 3.5 Temperature
Temperature is a measurement directly proportional to the average kinetic energy of particles. It determines the direction of heat transfer.
When two objects of different temperatures are in contact, heat moves from the object at the higher temperature to the object at lower temperature.
Almost all substances expand when they get hot and contract when the temperature decreases, or gets cold.

59. Temperature Scales Fahrenheit Celsius Kelvin
H2O Freezes at 32 ˚F and Boils at 212 ˚F
Celsius
H2O Freezes at 0 ˚C and Boils at 100 ˚C
Kelvin
H2O Freezes at 273 K and Boils at 373 K

61. Converting Temperature Scales
K = ºC
ºC = K –
ºC = 5/9 (ºF – 32)
ºF = 9/5 ºC + 32

62. Temperature
Absolute zero – the lowest possible theoretical temperature
Not reachable
All particles stop moving
Strange things happen

63. Examples
Convert 45 ˚C to K
Convert 55 ˚F to ˚C
Convert 82 ˚F to K

64. Chapter Recap 3.1 – The Importance of Measurement
Qualitative measurements: are not numerical
Quantitative: numerical measurements
Scientific Notation: 5 x 103
3.2 – Uncertainty in Measurements
Precision: consistency Accuracy: closeness to actual value
Error: difference between measurement and actual value
3.3 – International System of Units
Length: base unit is meter (m) volume: derived unit - cubic meters (m3) mass: base unit is kilogram (kg)
3.4 – Density
Density: amount of matter in a certain amount of space
D=m/V
3.5 – Temperature
Temperature: is proportional to the average kinetic energy of particles
Celsius: metric scale Kelvin: SI scale and also absolute scale