1. Measurements and their uncertainty

2. Convert measurements to scientific notation
Objectives
Convert measurements to scientific notation
Distinguish among accuracy, precision and error of measurement
Determine the number of significant figures in a measurement and in a calculated answer

3. Definition – quantity that has both a number and a unit
Measurements
Definition – quantity that has both a number and a unit
Measurements are made every day:
Buying products
Sports activities
Cooking

4. Qualitative – measurements are words, not numbers – hot, heavy
Measurement types
2 types of measurements
Qualitative – measurements are words, not numbers – hot, heavy
Quantitative – measurements involve numbers and depends on:
Reliability of measuring instrument
The care with which it is read

5. Number is written as the product of two numbers: A coefficient
Scientific Notation
Number is written as the product of two numbers:
A coefficient
10 raise to a power
Example:
602,000,000,000,0000,0000,000,000
6.02 x 1023

6. Accuracy, Precision, and Error
Accuracy – how close measurement is to true value
Measured value must be compared to correct value
Precision – how close the measurements are to each other
Compare values of two or more repeated measurements (reproducible)

7. Precision vs. Accuracy

9. Accepted value – correct value based on reliable references
Determining Error
Accepted value – correct value based on reliable references
Example: Density table pg 90
Experimental value – value measure in the lab

10. Error – difference between experimental value and accepted value
Determining Error
Error – difference between experimental value and accepted value
Error = exp. value – accepted value
Error can be either positive or negative

11. Percent error = |error| accepted value
Percent error – absolute value of error divided by the accepted value multiplied by 100
Percent error = |error|
accepted
value
x 100

12. Sample Problem
For a boiling point measurement of water in the lab you read 99.1 oC. What is the percent error?

13. Sample Problem
For a boiling point measurement of water in the lab you read 99.1 oC. What is the percent error?
Answer: 0.9%

14. Why Is There Uncertainty?
Measurements are performed with instruments
No instrument can be read to an infinite number of decimal places

15. Why Is There Uncertainty?
Which of these has the greatest uncertainty?

16. Significant Figures
Significant digits – in a measurement it includes all of the digits that are unknown plus a last digit that is estimated
Measurements are reported in correct sig figs b/c calculated answers depend on number of sig figs in the values used in the calculations

17. Figure 3.5 Significant Figures - Page 67
Which measurement is the best?

18. Non – zeros always count as significant figures:
Sig Fig Rules
Non – zeros always count as significant figures:
3456
4 sig figs

19. Leading zeros do not count as significant figures
Sig Fig Rules
Zeros
Leading zeros do not count as significant figures
0.0486
3 sig figs

20. Captive zeros always count as significant figures
Sig Fig Rules
Zeros
Captive zeros always count as significant figures
16.07
4 sig figs

21. Sig Fig Rules
Zeros
Trailing zeros are significant only if the number contains a decimal point
4 sig figs 2 sig figs

22. Two special situations – have unlimited number of sig figs
Sig Fig Rules
Two special situations – have unlimited number of sig figs
Counted items
23 people, 435 thumbtacks
Exactly defined quantities
60 minutes = 1 hour

24. How many sig figs in the following? 1.0070 m 17.10 kg 100890 L
Sig Fig Practice
How many sig figs in the following? m
17.10 kg L
3.29 x 103 s cm
3,200,000 mL
5 dogs

25. Sig Figs in Calculations
A calculated answer cannot be more precise than the least precise measurement from which it was calculated
The chain is only as strong as its weakest link
Calculated values need to be rounded

26. Decide how many sig figs are needed
Rounding
Decide how many sig figs are needed
Round to that many digits counting from the left!
Is the next digit <5? Drop it
Is the next digit >5? Increase by 1

27. Problems
Round off each measurement to the number of sig figs shown in ( ). Write the answers in scientific notation.
(four)
(two)
8792 (two)

28. Rounding – Addition and Subtraction
Answer should be rounded to same number of decimal places as the LEAST number of decimal places in problem
Problem:
Calculate the sum:
12.52 m m m

29. Rounding – Addition and Subtraction
Answer should be rounded to same number of decimal places as the LEAST number of decimal places in problem
Problem:
Calculate the sum:
12.52 m m m
369.8 m

30. Rounding – Multiplication and Division
Round the answer to the same number of significant figures as the LEAST number of sig figs in the problem
How many sig figs for the following operations:
7.55 x 0.34 meters
2.10 x 0.70 meters
2.4526/8.4

31. Rounding – Multiplication and Division
Round the answer to the same number of significant figures as the LEAST number of sig figs in the problem
How many sig figs for the following operations:
7.55 x 0.34 meters  2 sig figs
2.10 x 0.70 meters  2 sig figs
2.4526/8.40  3 sig figs

32. Section Assessment
A technician experimentally determined the boiling point of octane to be oC. The actual BP is oC. Calculate the error and percent error.

33. Determine the number of sig figs in the following: 11 soccer players
Section Assessment
Determine the number of sig figs in the following:
11 soccer players
10,800 meters
meters
5.00 cubic meters

34. The International System of Units

35. List SI units of measurement and common SI prefixes
Objectives
List SI units of measurement and common SI prefixes
Distinguish between the mass and weight of an object
Convert between Celsius and Kelvin temperature scales

36. International System of Units
SI – from French name
Measurements depend on units that are used as reference standards
In chemistry we use metric system

37. SI units normally used in chemistry:
5 SI Base Units
SI units normally used in chemistry:
Quantity
SI base unit
Symbol
Length
Meter m
Mass
Kilogram kg
Temperature
Kelvin K
Time
Seconds s
Amount of substance
Mole
mol

38. Nature of Measurements
Measurement – quantitative observation consisting of 2 parts:
Number
Unit
Example: 20 grams or 20 g

39. Non-SI units are used in chemistry as well: Liter – volume
Celsius – temperature
Calorie - heat

40. Million thousand tenth hundredth thousandth millionth billionth
Common SI Prefixes
Prefix
Abbreviation
Meaning
Exponent
Mega- M
Million
106
Kilo- k
thousand
103
Deci- d
tenth
10-1
Centi- c
hundredth
10-2
Milli- m
thousandth
10-3
Micro- 
millionth
10-6
Nano- n
billionth
10-9
Pico- P
trillionth
10-12

41. Most common metric units of length are: Centimeter – cm Meter – m
SI unit – meter
Measured using rulers
Most common metric units of length are:
Centimeter – cm
Meter – m
Kilometer - km

42. Space occupied by sample of matter
Volume
Space occupied by sample of matter
Calculated from a solid by multiplying length x width x height
Thus, SI is cubic meter or cm3
We normally use liters for volume
1 mL = 1 cm3

43. Graduated cylinder Pipets Burets Volumetric flask Syringes
Measuring Volume
Graduated cylinder
Pipets
Burets
Volumetric flask
Syringes

44. With an increase in temperature, the volume also increases
Volume Changes
With an increase in temperature, the volume also increases
Seen most in gases
Instruments are calibrated for 20 oC which is room temperature

45. Mass – measure of the quantity of matter present
Units of Mass
Mass – measure of the quantity of matter present
Weight – force that measures the pull by gravity – changes with location

46. SI unit for mass is kg – we commonly use grams in the laboratory
Measuring Mass
SI unit for mass is kg – we commonly use grams in the laboratory
Mass is measured using a triple beam balance (or electric balance)

47. Measure of how hot or cold something is
Temperature
Measure of how hot or cold something is
Heat moves from object of higher temperature to object of lower temp
2 units used:
Kelvin
Celsius

48. Celsius scale defined by two readily determined temperatures:
Freezing point of water = 0 oC
Boiling point of water = 100 oC
Kelvin scale does not use the degree sign, but is just represented by K
absolute zero = 0 K (thus no negative values)
formula to convert: K = oC + 273

49. Sample Problem
Normal human body temperature is 37 oC. What is the temperature in Kelvin?

50. Energy is the capacity to do work or produce heat
Energy can be measured using:
Joule (J) – the SI unit for energy
Calorie (cal) – the heat needed to raise 1 gram of water by 1 oC

51. Energy
Conversions between Joules and Calories can be carried out by using the following relationship:
1 cal = J

52. Section Assessment
Name the quantity measured by each of the SI base units and give the SI symbol of the unit.

53. Conversion Problems

54. Construct conversion factors from equivalent measurements
Objectives
Construct conversion factors from equivalent measurements
Apply the technique of dimensional analysis to a variety of conversion problems
Solve problems by breaking the solution into steps
Convert complex units, using DA

55. A “ratio” of equivalent measurements
Conversion Factors
A “ratio” of equivalent measurements
Start with 2 things that are the same:
1 meter = 100 centimeters

56. Write 2 conversion factors for the following:
Practice
Write 2 conversion factors for the following:
Between kilograms and grams
Between feet and inches
Using qt = 1.00 L

57. Why Use Conversion Factors?
We can multiply them to change the units
Question: 13 inches is how many yards?
We know that 36 inches = 1 yard

58. A way to analyze and solve problems by using units of measurement
Dimensional Analysis
A way to analyze and solve problems by using units of measurement
Dimension = a unit
Analyze = to solve
Using units so solve the problems

59. A ruler is 12.0 inches long. How long is it in cm? ( 1 inch = 2.54 cm)
Dimensional Analysis
DA provides alternative approach to problem solving, instead of with equation or algebra.
A ruler is 12.0 inches long. How long is it in cm? ( 1 inch = 2.54 cm)
How long is this in meters?
A race is 10.0 km long. How far is this in miles, if:
1 mile = 1760 yards
1 meter = yards

60. How many minutes are there in a week?
Problem
How many minutes are there in a week?

61. Problem
An experiment requires that each student use an 8.5-cm length of magnesium ribbon. How many students can do the experiment if there is a 570-cm length of magnesium ribbon available?

62. Problem
Convert:
0.044 km to m
4.6 mg to g
0.107 g to cg

63. Complex units – units that are expressed as a ratio of two units
Speed – meters/hour
Sample problem: Change 15 m/hr to cm/s

64. Density

65. Calculate the density of a material from experimental data
Objectives
Calculate the density of a material from experimental data
Describe how density varies with temperature

66. Density – relationship between mass and volume Formula Density = mass
Common units: g/mL or g/cm3

67. Density
If you recall, density is a physical property so it does not depend on sample size

68. Density and Temperature
What happens to density as the temperature of an object increases?
Mass remains the same
Increase in volume as temperature increases
Density DECREASES as temperature increases

69. Water is an exception to the density rule
Density and Water
Water is an exception to the density rule
Over certain temperatures, the volume of water increases as the temperature decreases
Does ice float in liquid water?
Why?

70. Section Assessment
A 68 g bar of gold is cut into 3 equal pieces. How does the density of each piece compare to the density of the original gold bar?

71. Section Assessment
What is the volume, in cubic centimeters, of a sample of cough syrup that has a mass of 50.0 g? The density of cough syrup is g/cm3