Appendix 1 - Units and Converstion Factors
- Page ID
- 52104
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Wherever possible, this text uses metric units of measurement. The metric system of measurement is used by all major countries but the United States, and it is the universal system used by all scientists. At present, an additional process is under way directed toward using only those metric units that are standard units approved in the International System of units (SI units). However, some of these standard units are unfamiliar even to many scientists, so they are not yet universally used. SI units are used in this text if they are generally in wide usage. In some instances where nonstandard units are much more widely used in the United States, the nonstandard units are used in this text. Over time, there will likely be a migration to the universal and exclusive use of SI units. The SI unit system has only seven base units from which all other units are derived (derived units are combinations of the base units). Tables listing the base units of the SI system, some derived SI units, and all of the units used in this text are included in this appendix. Some conversion factors to relate the SI units and other metric units to other units commonly used in the United States are also included.
The scientific community almost universally uses exponential notation for numbers. Exponential notation is explained in Chapter 1 and is used throughout this text. This appendix includes a table (“Exponential Notation and the Decimal System”) for converting exponential numbers to their nonexponential equivalents. To multiply numbers expressed exponentially, add the exponents (superscript numbers). For example, 10–1 × 103 = 102 (one-tenth of 1000 is equal to 100). To divide, subtract the exponents. The “SI Base Units” table also lists the common terms used to identify certain exponent values. For example, 1000 is equivalent to 103, or 1 × 103, and 1000 can be expressed as “one thousand,” while other units can be prefixed by “kilo-” to express one thousand of the units; for example, 1 kilogram is equal to 1000 grams.
Note that the naming system for large and small numbers is different in different parts of the world. In many non-English-speaking countries (and formerly in England), the term billion does not mean 109. Instead, in this alternate system billion is 1012 and trillion is 1018. This is one reason why it is always better to use exponential notation for large or small numbers.
SI Base Units
| Parameter | Unit | Symbol |
|---|---|---|
| Length | meter | m |
| Mass | gram | g |
| Time | second | s |
| Electrical current | ampere | A |
| Thermodynamic temperature | kelvin | K |
| Amount of substance | molea | mol |
| Luminous intensity | candela | cd |
a1 mol is equal to the molecular weight in grams
Examples of Derived SI Units
| Derived Quantity | Name | Symbol |
|---|---|---|
| Area | square meter | m2 |
| Volume | cubic meter | m3 |
| Speed, velocity | meter per second | m·s–1 |
| Acceleration | meter per second squared | m·s–2 |
| Mass density | kilogram per cubic meter | kg·m–3 |
| Specific volume | cubic meter per kilogram | m3·kg–1 |
| Current density | ampere per square meter | A·m–2 |
| Magnetic field strength | ampere per meter | A·m–1 |
| Amount-of-substance concentration | mole per cubic meter | mol·m–3 |
| Luminance | candela per square meter | cd·m–2 |
| Mass fraction | kilogram per kilogram, which may be represented by the number 1 |
kg·kg–1 = 1 |
SI Derived Units with Special Names and Symbols
| Derived Quantity | Name | Symbol | Expression in Terms of Other SI Units | Expression in Terms of SI Base Units |
|---|---|---|---|---|
| Plane angle | radian | rad | — | m · m–1 = 1 |
| Frequency | hertz | Hz | — | s–1 |
| Force | newton | N | — | m · kg · s–2 |
| Pressure, stress | pascal | Pa | N · m–2 | m–1 · kg · s–2 |
| Energy, work, quantity of heat | joule | J | N · m | m2 · kg · s–2 |
| Power, radiant flux | watt | W | J · s | m2 · kg · s–3 |
| Celsius temperature | degree Celsius | °C | — | K |
| Luminous flux | lumen | lm | cd · sr | m2 · m–2 · cd = cd |
| Illuminance | lux | lx | lm · m2 | m2 · m–4 · cd = m–2 · cd |
| Activity (of a radionuclide) | becquerel | Bq | — | s–1 |
For ease of understanding and convenience, a few SI derived units have been given special names and symbols. These are some that are relevant to this text.
Exponential Notation and the Decimal System
| Value | Exponential Expression | Name | Prefix |
|---|---|---|---|
| 1,000,000,000,000 | 1012 | 1 trillion | tera- |
| 1,000,000,000 | 109 | 1 billion | giga- |
| 1,000,000 | 106 | 1 million | mega- |
| 1,000 | 103 | 1 thousand | kilo- |
| 100 | 102 | 1 hundred | centa- |
| 10 | 101 | ten | deca- |
| 1 | 100 | one | uni- |
| 0.1 | 10–1 | 1 tenth | deci- |
| 0.01 | 10–2 | 1 hundredth | centi- |
| 0.001 | 10–3 | 1 thousandth | milli- |
| 0.000,001 | 10–6 | 1 millionth | micro- |
| 0.000,000,001 | 10–9 | 1 billionth | nano- |
| 0.000,000,000,001 | 10–12 | 1 trillionth | pico- |
Conversions between Basic Units of Length, Mass, and Time
Length
1 kilometer = 1000 meters (m)
1 meter = 100 centimeters (cm)
1 centimeter = 10 millimeters (mm)
1 millimeter = 10 micrometers (mm)
1 micrometer = 10 nanometers (nm)
Mass
1 tonne (metric ton) = 1000 kilograms (kg)
1 kilogram = 1000 grams (g)
1 gram = 10 milligrams (mg)
1 milligram = 10 micrograms (mg)
1 microgram = 10 nanograms (ng)
1 nanogram = 10 picograms (pg)
Time
1 hour = 3600 seconds (s)
Units of Measurement Used in this Text
- Length/distance
- meter (m) — SI base unit
- millimeter (mm)
- centimeter (cm)
- kilometer (km)
- foot (ft.) — obsolete nonmetric unit
- nautical mile (n.m.) — equals 1.853 km (1.15 statute mi.) or 1 min (1/60 of a degree) of longitude
- Mass
- kilogram (kg) — SI base unit
- gram (g)
- milligram (mg)
- microgram (mg)
- tonne (t) — metric ton, equal to 103 kg
- Time
- second (s) — SI base unit
- year (yr)
- day (day)
- hour (h)
- minute (min)
- Area
- meter squared (m2) — derived SI unit
- centimeter squared (cm2)
- kilometer squared (km2)
- Volume
- meter cubed, cubic meters (m3) — derived SI unit
- centimeter cubed (cm3)
- kilometer cubed (km3)
- liter (l) — equals 10 cm3, so 1 m3 = 1000 l
- Pressure
- pascal (Pa) — derived SI unit (not used in this text)
- kilogram per centimeter squared (kg · cm–2) — equals 9.56 × 106 Pa
- atmosphere (atm) — equals 1.03 kg · cm–2
- Mass density (absolute density)
- kilogram per cubic meter (kg · m–3) — derived SI unit
- gram per cubic centimeter (g · cm–3)
- Speed/velocity
- meters per second (m · s–1) — derived SI unit
- centimeters per second (cm · s–1)
- kilometers per hour (km · h–1) — 1 km · h–1 = 0.28 m · s–1= 28 cm · s–1
- kilometers per day (km · day–1)
- Acceleration
- meters per second per second (m · s–2) — derived SI unit
- Temperature
- degrees Celsius (°C)
- Energy and related unites
- joule (J) — derived SI unit
- joule per meter squared (J · m–2) — used as measure of wave energy
- joule per gram (J · g–1) — used as measure of latent heat
- joule per gram per degree Celsius (J · g–1 · °C–1) — used as measure of heat capacity
- calorie (cal) — obsolete measure of energy
- calories per gram (cal · g–1) — obsolete, used as measure of latent heat
- calories per gram per degree Celsius (cal · g–1 · °C–1) — obsolete, used as measure of heat capacity
- Concentration
- mole per cubic meter (mol · m3) — derived SI unit (not used in this text)
- milligram per kilogram (mg · kg–1)
- microgram per kilogram (mg · kg–1)
- Notes:
- Concentrations are expressed as mass of dissolved (or constituent) substance in one unit mass of the solution (or combined mixture)
- 1 mol is defined as the molecular weight of a substance expressed in grams. To convert concentration in mg · kg–1 to mol · m–3, divide by the molecular weight of the dissolved substance (or constituent); then divide by the solution (or mixture) density in kg · m3 and multiply by 1000
- Miscellaneous
- grams per year (g · yr–1) — mass transport rate
- cubic meters per second (m3 · s–1) — volume transport rate
- practical salinity unit — dimensionless ratio; no abbreviation, but sometimes listed as PSU
- millions of years ago (mya) — millions of years before the present date
- before the common era (BCE) — number of years before the year 1 of the Christian calendar, equivalent to BC
- the common era (CE) — number of years after the year 1 of the Christian calendar, equivalent to AD
Additional Conversations: Metric to Other Units
Length
1 km = 0.62 mi.
1 km = 0.54 n.m.
1 km = 1093 yard
1 m = 39.4 in.
1 m = 3.28 ft.
1 cm = 0.394 in.
Mass
1 kg = 2.2 lb
1 t = 2205 lb
1 t = 1.10 U.S. tons
1 g = 0.035 ounce
Area
1 km2 = 0.386 mi.2
1 km2 = 247.1 acres
1 m2 = 10.7 ft.2
1 cm2 = 0.155 in.2
Volume
1 m3 = 25.3 ft.3
1 m3 = 264 U.S. gallons
1 cm3 = 0.061 in.3
1 l = 2.12 pints
Pressure
1 kg · cm–2 = 14.2 lb · in.–2
1 kg · cm–2 = 0.97 atm
1 kg · cm–2 = 956 millibars
1 kg · cm–2 = 0.956 bar
1 kg · cm–2 = 956,000 Pa
1 kg · cm–2 = 29.0 in. of mercury at 0°C
1 kg · cm–2 = 737 mm of mercury at 0°C
Speed
1 km · h–1 = 0.62 mi. · h
1 km · h–1 = 0.54 knot
1 cm · s–1 = 1.97 ft. · min–1
1 cm · s–1 = 0.033 ft. · s–1
Temperature
0°C = 32°F
10°C = 50°F
20°C = 68°F
30°C = 86°F
40°C = 104°F
100°C = 212°F