# BOOK CONTENT

IIntroduction | 13 | |||

I | A History of Measurement | 15 | ||

II | The “Power of Ten” Notation | 17 | ||

1. | Standard notation | 18 | ||

2 | Expressing numbers in long form | 19 | ||

3. | Standard notation and the use of calculators | 20 | ||

Calculator displays | 20 | |||

Calculating powers | 21 | |||

4. | Manipulation of exponents | 22 | ||

5. | Worked examples | 23 | ||

6. | The range of distances in the universe in “power of ten” notation | 26 | ||

Test 1 – “Power of ten” notation | 27 | |||

Level 1 | 27 | |||

Level 2 | 28 | |||

Level 3 | 29 | |||

III | Physical Quantities, Units, Symbols and Prefixes | 31 | ||

1. | Table 1 – SI Prefixes | 32 | ||

2. | Rules relating to the presentation of SI quantities and their units | 34 | ||

Test 2A – SI prefixes | 36 | |||

Test 2B – SI prefixes | 38 | |||

IV | The International System of Units | 39 | ||

1. | The three basic standards in the SI system of measurement | 40 | ||

2. | Table 2 – Base and supplementary SI units | 41 | ||

3. | Table 3 – Comparison of the SI units and the fps units of distance | 43 | ||

4. | Table 4 – Derived SI units | 46 | ||

5. | Definitions of the main SI standard units | 48 | ||

6. | Table 5 – Other units | 52 | ||

7. | Conversion charts | 56 | ||

8. | The Greek alphabet | 57 | ||

Test 3 – Your vocabulary of units of measurement | 58 | |||

V | The Characteristics of the SI System | 61 | ||

VI | Conversion of Units | 67 | ||

1. | Worked examples | 67 | ||

Test 4 – Conversion exercises | 73 | |||

Level 1 | 73 | |||

Level 2 | 74 | |||

Level 3 | 75 | |||

Level 4 | 76 | |||

Level 5 | 77 | |||

VII | Measurement: Accuracy, Significant Figures, Uncertainties | 79 | ||

1. | Taking a reading | 80 | ||

2. | Significant figures | 81 | ||

3. | Accuracy and precision | 81 | ||

4. | Absolute and relative uncertainties | 82 | ||

5. | Significant figures and rounding off | 83 | ||

6. | The number of significant figures in calculations | 84 | ||

7. | Rounding off numbers | 85 | ||

8. | Presentation of numbers containing the digit zero | 86 | ||

Test 5 – Significant figures | 87 | |||

Level 1 | 87 | |||

Level 2 | 88 | |||

VIII | Types of Errors and Uncertainties in Measurement | 89 | ||

1. | Systematic uncertainty (SU) | 89 | ||

2. | Random uncertainty (RU) | 90 | ||

3. | Mistake error and other errors | 91 | ||

4. | Estimating uncertainty in a measured quantity due to its variation. Conclusion |
92 | ||

5. | Measuring instruments and uncertainties in measurements | 94 | ||

5.1 | Measuring with instruments | 94 | ||

Table 6 – The average uncertainty of common instruments | 96 | |||

5.2 | Indirect measurement | 100 | ||

Test 6 – Taking reading | 104 | |||

IX | Compound Errors | 107 | ||

1. | Compound errors in additions and subtractions | 107 | ||

2. | The number of significant figures in errors | 107 | ||

3. | Compound errors in division and multiplication | 108 | ||

4. | Compound errors in exponential expressions | 110 | ||

5. | Constant and counted values | 110 | ||

6. | Rounding off in complex mathematical operations | 112 | ||

7. | Uncertainty in a calculated result | 113 | ||

Test 7 – Errors and uncertainties | 114 | |||

X | Estimation | 117 | ||

1. | Estimating answers by approximating calculations | 118 | ||

2. | Estimating answers in complex calculations by scientific notations | 120 | ||

Test 8 – Estimation exercises | 122 | |||

Level 1 | 122 | |||

Level 2 | 123 | |||

Test 9 – (Gu)es(s)timation | 124 | |||

XI a) | Presentation of a Laboratory Report | 129 | ||

General guidelines | 129 | |||

XI b) | Report Presentation; Overview | 133 | ||

XII | Various Stages in Practical Work | 139 | ||

Stage 1 – Formulating the aim of the experiment | 139 | |||

Stage 2 – Designing and planning the experiment | 139 | |||

Stage 3 – Performing the experiment | 139 | |||

Stage 4 – Analysing the observations and measurements | 140 | |||

Stage 5 – Drawing the conclusion | 140 | |||

Stage 6 – Writing the report | 140 | |||

XIII | Problems | 141 | ||

XIV | Physical Constants | 143 | ||

XV | Formulae for Area and Volume | 145 | ||

XVI | Answers | 147 | ||

Test 1 – “Power of ten” notation | 149 | |||

Level 1 | 149 | |||

Level 2 | 150 | |||

Level 3 | 151 | |||

Test 2A – SI prefixes | 152 | |||

Test 2B – SI prefixes | 153 | |||

Test 3 – Your vocabulary of units of measurement | 154 | |||

Test 4 – Conversion exercises | 155 | |||

Level 1 | 155 | |||

Level 2 | 155 | |||

Level 3 | 156 | |||

Level 4 | 157 | |||

Level 5 | 158 | |||

Test 5 – Significant figures | 159 | |||

Level 1 | 159 | |||

Level 2 | 160 | |||

Test 6 – Taking readings | 161 | |||

Test 7 – Errors and uncertainties | 162 | |||

Test 8 – Estimation exercises | 166 | |||

Level 1 | 166 | |||

Level 2 | 167 | |||

Test 9 – (Gu)es(s)timation | 168 | |||

Answers to puzzles | 172 | |||

Conversion Tables | 175 | |||

Bibliography | 179 | |||

US Metric Association on metric conversion in USA | 181 | |||

Reviews | 183 | |||

Articles | 185 |