PART I
UNITS
Units are labels that are used to distinguish one type of measurable quantity from other types. Length, mass, and time are distinctly different physical quantities, and therefore have different unit names, such as meters, kilograms and seconds. We use several systems of units, including the metric (SI), the English (or U.S. customary units), and a number of others, which are of mainly historical interest.
This part of the book contains the following:
• International System of Units
• Metric Units of Measurement
• U.S. Units of Measurement
• Units of Measure in Precious Metals
• Tables of Equivalents
INTERNATIONAL SYSTEM OF UNITS
The International System of Units, abbreviated as SI, is the modernized version of the metric system established by international agreement.
1. SI Base Units
| Quantity | Name | Symbol |
| length | meter | m |
| mass | kilogram | kg |
| time | second | s |
| electric current | ampere | A |
| thermodynamic temperature | kelvin | K |
| amount of a substance | mole | mol |
2. SI Derived Units
| Quantity | Name | Symbol |
| area | square meter | m2 |
| volume | cubic meter | m3 |
| speed, velocity | meter per second | m/s |
| acceleration | meter per second squared | m/s2 |
| wave number | reciprocal meter | m−1 |
| mass density | kilogram per cubic meter | kg/m3 |
| specific volume | cubic meter per kilogram | m3/kg |
| current density | ampere per square meter | A/m2 |
| magnetic field strength | ampere per meter | A/m |
| amount-of-substance concentration | mol per cubic meter | mol/m3 |
| luminance | candela per square meter | cd/m2 |
| mass fraction | kilogram per kilogram | kg/kg |
3. SI Derived Units with Special Names and Symbols
| Quantity | Name | Symbol |
| plane angle | radian | rad |
| solid angle | steradian | sr |
| frequency | hertz | Hz |
| force | newton | N |
| pressure, stress | pascal | Pa |
| energy, work, quantity of heat | joule | J |
| power, radiant flux | watt | W |
| electric charge, quantity of electricity | coulomb | C |
| electric potential difference | volt | V |
| capacitance | farad | F |
| electric resistance | ohm | Ω |
| electric conductance | siemens | S |
| magnetic flux | weber | Wb |
| magnetic flux density | tesla | T |
| inductance | henry | H |
| Celsius temperature | degree Celsius | °C |
| luminous flux | lumen | lm |
| illuminance | lux | lx |
| activity of a radionuclide | becquerel | Bq |
| absorbed dose, specific energy, kerma | gray | Gy |
| dose equivalent | sievert | Sv |
| catalytic activity | katal | kat |
4. SI Derived Units Whose Names and Symbols Include SI Derived Units with Special Names and Symbols
| Quantity | Name | Symbol |
| dynamic viscosity | pascal second | Pa · s |
| moment of force | newton meter | N · m |
| angular velocity | radian per second | rad/s |
| angular acceleration | radian per second squared | rad/s2 |
| heat flux density, irradiance | watt per square meter | W/m2 |
| heat capacity, entropy | joule per kelvin | J/K |
| specific heat capacity, specific entropy | joule per kilogram kelvin | J/(kg · K) |
| specific energy | joule per kilogram | J/kg |
| energy density | joule per cubic meter | J/m3 |
| thermal conductivity | watt per meter kelvin | W/(m · K) |
| electric field strength | volt per meter | V/m |
| electric charge density | coulomb per cubic meter | C/m3 |
| electric flux density | coulomb per square meter | C/m2 |
| permittivity | farad per meter | F/m |
| permeability | henry per meter | H/m |
| molar energy | joule per mole | J/mol |
| molar entropy, molar heat capacity | joule per mole kelvin | J/(mol · K) |
| exposure (X and γ rays) | coulomb per kilogram | C/kg |
| absorbed dose rate | gray per second | Gy/s |
| radiant intensity | watt per steradian | W/sr |
| radiance | watt per square meter steradian | W/(m2 · sr) |
5. Units Outside the SI that Are Accepted for Use with the SI
| Name | Symbol | Value in SI units |
| minute | min | 1 min = 60 s |
| hour | h | 1 h = 60 min = 3600 s |
| day | d | 1 d = 24 h = 86400 s |
| liter | L | 1 L = 1 dm3 = 10−3 m3 |
| metric tone | t | 1 t = 103 kg |
| bel | B | 1 B = 10 dB |
| degree (angle) | ° | 1° = (π/180) rad |
| minute (angle) | ′ | 1′ = (1/60)° = = (π/10800) rad |
| second (angle) | ″ | 1″ = (1/60)′ = = (π/648000) rad |
| electronvolt | eV | 1 eV = 1.60218 × 10−19 J |
| unified atomic mass unit | u | 1 u = 1.66054 × 10−27 kg |
| astronomical unit | ua | 1 ua = 1.49598 × 1011 m |
| nautical mile | | 1 nautical mile = 1852 m |
| knot | | 1 knot = 1852/3600 m/s |
| are | a | 1 a = 100 m2 |
| hectare | ha | 1 ha = 100 a = 104 m2 |
| bar | bar | 1 bar = 102 kPa = 105 Pa |
| angstrom | Å | 1 Å = 0.1 nm = 10−10 m |
| curie | Ci | 1 Ci = 3.7 × 1010 Bq |
| rad | rad | 1 rad = 10−2 Gy |
| rem | rem | 1 rem = 10−2 Sv |
6. SI Prefixes
| Factor | Name | Symb. | Factor | Name | Symb. |
| 101 | deca | da | 10−1 | deci | d |
| 102 | hecto | h | 10−2 | centi | c |
| 103 | kilo | k | 10−3 | milli | m |
| 106 | mega | M | 10−6 | micro | μ |
| 109 | giga | G | 10−9 | nano | n |
| 1012 | tera | T | 10−12 | pico | P |
| 1015 | peta | P | 10−15 | femto | f |
| 1018 | exa | E | 10−18 | atto | a |
METRIC UNITS OF MEASUREMENT
The metric system was first proposed in 1791. The French Revolutionary Assembly adopted it in 1795, and the first metric standards (a standard meter bar and kilogram bar) were adopted in 1799.
7. Units of Length
| Name | Symbol | Value |
| millimeter | mm | 1 mm = 0.001 m |
| centimeter | cm | 1 cm = 10 mm |
| decimeter | dm | 1 dm = 10 cm |
| meter | m | 1 m = 10 dm = 1000 mm |
| dekameter | dam | 1 dam = 10 m |
| hectometer | hm | 1 hm = 10 dam |
| kilometer | km | 1 km = 10 hm = 1000 m |
8. Units of Area
| Name | Symbol | Value |
| sq. millimeter | mm2 | 1 mm2 = 0.000001 m2 |
| sq. centimeter | cm2 | 1 cm2 = 100 mm2 |
| sq. decimeter | dm2 | 1 dm2 = 100 cm2 |
| sq. meter | m2 | 1 m2 = 100 dm2 |
| sq. decameter | dam2 | 1 dam2 = 100 m2 |
| sq. hectometer | hm2 | 1 hm2 = 100 dam2 |
| sq. kilometer | km2 | 1 km2 = 100 hm2 |
9. Units of Liquid Value
| Name | Symbol | Value |
| milliliter | mL | 1 mL = 0.001 L |
| centiliter | cL | 1 cL = 10 mL |
| deciliter | dL | 1 dL = 10 cL |
| liter | L | 1 L = 10 dL = 1000 mL |
| dekaliter | daL | 1 daL = 10 L |
| hectoliter | hL | 1 hL = 10 daL |
| kiloliter | kL | 1 kL = 10 hL = 1000 L |
10. Units of Volume
| Name | Symbol | Value |
| cu. millimeter | mm3 | 1 mm3 = 10 −9 m3 |
| cu. centimeter | cm3 | 1 cm3 = 1000 mm3 |
| cu. decimeter | dm3 | 1 dm3 = 1000 cm3 |
| cu. meter | m3 | 1 m3 = 1000 dm3 |
11. Units of Mass
| Name | Symbol | Value |
| milligram | mg | 1 mg = 0.001 g |
| centigram | cg | 1 cg = 10 mg |
| decigram | dg | 1 dg = 10 cg |
| gram | g | 1 g = 10 dg |
| dekagram | dag | 1 dag = 10 g |
| hectogram | hg | 1 hg = 10 dag |
| kilogram | kg | 1 kg = 10 hg = 1000 g |
| megagram | Mg | 1 Mg = 1000 kg = 1 t |
U.S. UNITS OF MEASUREMENT
Most of the U.S. system of measurements is the same as that forthe U.K. The biggest differences to be noted are that the present British gallon and bushel—known, as the “Imperial gallon” and the “Imperial bushel”—are, respectively, about 20 percent and 3 percent larger than the U.S. gallon and bushel.
12. Units of Length
| Name | Symbol | Value |
| inch | in | 1 in = 0.83333 ft |
| foot | ft | 1 ft = 12 in |
| yard | yd | 1 yd = 3 ft |
| rod | rd | 1 rd = 16.5 ft |
| furlong | fur | 1 fur = 40 rd |
| U.S. mile | mi | 1 mi = 8 fur = 5280 ft |
| nautical mile | nautical mile | 1 nautical mile = 1852 m = 6076.1149 ft (approx.) |
13. Units of Area
| Name | Symbol | Value |
| sq. inch | in2 | 1 in2 = 0.006444 ft2 |
| sq. foot | ft2 | 1 ft2 = 144 in2 |
| sq. yard | yd2 | 1 yd2 = 9 ft2 |
| sq. rod | rd2 | 1 rd2 = 272.25 ft2 |
| acre | acre | 1 acre = 160 rd = 43 560 ft2 |
| sq. mile | mi2 | 1 mi2 = 640 acre |
| township | | 1 township = 6 mi2 |
14. Units of Liquid Volume
| Name | Symbol | Value |
| gill | gi | 1 gi = 0.25 pt |
| pint | pt | 1 pt = 4 gi |
| quart | qt | 1 qt = 2 pt |
| gallon | gal | 1 gal = 4 qt = 8 pt = 32 gi |
15. Units of Volume
| Name | Symbol | Value |
| cu. inch | in3 | 1 in3 = 0.0005787 ft3 |
| cu. foot | ft3 | 1 ft3 = 1728 in3 |
| cu. yard | yd3 | 1 yd3 = 27 ft3 |
16. Apothecaries’ Units of Liquid Volume
| Name | Symbol | Value |
| minim | min | 1 min = 0.016666 dr |
| fluid dram | fl dr | 1 fl dr = 60 min |
| fluid ounce | fl oz | 1 fl oz = 8 fl dr |
| pint | pt | 1 pt = 16 fl oz |
| quart | qt | 1 qt = 2 pt |
| gallon | gal | 1 gal = 4 qt |
17. Units of Dry Volume
