| IIntroduction |
13 |
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| I |
A History of Measurement |
15 |
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| II |
The “Power of Ten” Notation |
17 |
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1. |
Standard notation |
18 |
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2 |
Expressing numbers in long form |
19 |
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3. |
Standard notation and the use of calculators |
20 |
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Calculator displays |
20 |
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Calculating powers |
21 |
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4. |
Manipulation of exponents |
22 |
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5. |
Worked examples |
23 |
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6. |
The range of distances in the universe in “power of ten” notation |
26 |
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Test 1 – “Power of ten” notation |
27 |
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Level 1 |
27 |
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Level 2 |
28 |
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Level 3 |
29 |
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| III |
Physical Quantities, Units, Symbols and Prefixes |
31 |
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1. |
Table 1 – SI Prefixes |
32 |
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2. |
Rules relating to the presentation of SI quantities and their units |
34 |
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Test 2A – SI prefixes |
36 |
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Test 2B – SI prefixes |
38 |
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| IV |
The International System of Units |
39 |
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1. |
The three basic standards in the SI system of measurement |
40 |
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2. |
Table 2 – Base and supplementary SI units |
41 |
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3. |
Table 3 – Comparison of the SI units and the fps units of distance |
43 |
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4. |
Table 4 – Derived SI units |
46 |
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5. |
Definitions of the main SI standard units |
48 |
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6. |
Table 5 – Other units |
52 |
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7. |
Conversion charts |
56 |
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8. |
The Greek alphabet |
57 |
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Test 3 – Your vocabulary of units of measurement |
58 |
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| V |
The Characteristics of the SI System |
61 |
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| VI |
Conversion of Units |
67 |
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1. |
Worked examples |
67 |
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Test 4 – Conversion exercises |
73 |
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Level 1 |
73 |
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Level 2 |
74 |
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Level 3 |
75 |
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Level 4 |
76 |
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Level 5 |
77 |
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| VII |
Measurement: Accuracy, Significant Figures, Uncertainties |
79 |
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1. |
Taking a reading |
80 |
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2. |
Significant figures |
81 |
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3. |
Accuracy and precision |
81 |
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4. |
Absolute and relative uncertainties |
82 |
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5. |
Significant figures and rounding off |
83 |
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6. |
The number of significant figures in calculations |
84 |
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7. |
Rounding off numbers |
85 |
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8. |
Presentation of numbers containing the digit zero |
86 |
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Test 5 – Significant figures |
87 |
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Level 1 |
87 |
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Level 2 |
88 |
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| VII |
Types of Errors and Uncertainties in Measurement |
89 |
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1. |
Systematic uncertainty (SU) |
89 |
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2. |
Random uncertainty (RU) |
90 |
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3. |
Mistake error and other errors |
91 |
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4. |
Estimating uncertainty in a measured quantity due to its variation Conclusion |
92 |
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5. |
Measuring instruments and uncertainties in measurements |
94 |
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5.1 |
Measuring with instruments |
94 |
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Table 6 – The average uncertainty of common instruments |
96 |
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5.2 |
Indirect measurement |
100 |
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Test 6 – Taking reading |
104 |
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| IX |
Compound Errors |
107 |
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1. |
Compound errors in additions and subtractions |
107 |
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2. |
The number of significant figures in errors |
107 |
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3. |
Compound errors in division and multiplication |
108 |
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4. |
Compound errors in exponential expressions |
110 |
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5. |
Constant and counted values |
110 |
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6. |
Rounding off in complex mathematical operations |
112 |
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7. |
Uncertainty in a calculated result |
113 |
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Test 7 – Errors and uncertainties |
114 |
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| X |
Estimation |
117 |
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1. |
Estimating answers by approximating calculations |
118 |
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2. |
Estimating answers in complex calculations by scientific notations |
120 |
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Test 8 – Estimation exercises |
122 |
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Level 1 |
122 |
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Level 2 |
123 |
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Test 9 – (Gu)es(s)timation |
124 |
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| XI |
Presentation of a Laboratory Report |
129 |
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General guidelines |
129 |
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| XII |
Various Stages in Practical Work |
133 |
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Stage 1 – Formulating the aim of the experiment |
133 |
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Stage 2 – Designing and planning the experiment |
133 |
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Stage 3 – Performing the experiment |
133 |
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Stage 4 – Analysing the observations and measurements |
134 |
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Stage 5 – Drawing the conclusion |
134 |
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Stage 6 – Writing the report |
134 |
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| XIII |
Problems |
135 |
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| XIV |
Physical Constants |
137 |
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| XV |
Formulae for Area and Volume |
139 |
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| XVI |
Answers |
141 |
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Test 1 – “Power of ten” notation |
143 |
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Level 1 |
143 |
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Level 2 |
144 |
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Level 3 |
145 |
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Test 2A – SI prefixes |
146 |
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Test 2B – SI prefixes |
147 |
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Test 3 – Your vocabulary of units of measurement |
148 |
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Test 4 – Conversion exercises |
149 |
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Level 1 |
149 |
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Level 2 |
149 |
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Level 3 |
150 |
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Level 4 |
151 |
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Level 5 |
152 |
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Test 5 – Significant figures |
153 |
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Level 1 |
153 |
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Level 2 |
154 |
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Test 6 – Taking readings |
155 |
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Test 7 – Errors and uncertainties |
156 |
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Test 8 – Estimation exercises |
160 |
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Level 1 |
160 |
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Level 2 |
161 |
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Test 9 – (Gu)es(s)timation |
162 |
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Answers to puzzles |
166 |
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Conversion Tables |
169 |
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Bibliography |
173 |
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US Metric Association on metric conversion in USA |
175 |
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Reviews |
177 |