APPENDIX A Systems of Measurement

I THE SI SYSTEM mass. A pound (avdp), lb, is a unit of weight. On the sur- face of the Earth, 1 lb is equal to 0.454 kg. A metric ton,

In the past, scientists from different parts of the also written as tonne, is 1000 kg, or about 2205 lb. world have used different systems of measurement.

However, global cooperation and communication make Temperature The Celsius scale is used in most labora- it essential to adopt a standard system. The International tories to measure temperature. On the Celsius scale the System of Units (SI) defines various units of measure- freezing point of water is 0ºC and the boiling point of ment as well as prefixes for multiplying or dividing the

water is 100ºC.

units by decimal factors. Some primary and derived units The SI unit of temperature is the Kelvin. The cold- important to geologists are listed below. est possible temperature, which is ⫺273ºC, is zero on the

Time

Kelvin scale. The size of 1 degree Kelvin is equal to 1 The SI unit is the second, s or sec, which used to

degree Celsius.

be based on the rotation of the Earth but is now related to the vibration of atoms of cesium-133. SI prefixes are

used for fractions of a second (such as milliseconds or Celsius temperature (ºC) ⫽ Kelvin temperature (K) ⫺ 273 K

microseconds), but the common words minutes, hours, and days are still used to express multiples of seconds.

Fahrenheit temperature (ºF) is not used in scientific writing, although it is still popular in English-speaking

Length The SI unit is the meter, m, which used to be countries. Conversion between Fahrenheit and Celsius is based on a standard platinum bar but is now defined in

shown below.

terms of wavelengths of light. The closest English equivalent is the yard (0.914 m). A mile is 1.61 kilometers

°F

°C

(km). An inch is exactly 2.54 centimeters (cm).

Area Area is length squared, as in square meter,

square foot, and so on. The SI unit of area is the are, a, which is 100 sq m. More commonly used is the hectare, 200 90

ha, which is 100 ares, or a square that is 100 m on each

side. (The length of a U.S. football field plus one end

zone is just about 100 m.) A hectare is 2.47 acres. An 70 acre is 43,560 sq ft, which is a plot of 220 ft by 198 ft,

for example.

Volume 40

Volume is length cubed, as in cubic centime- ter, cm 3 , cubic foot, ft 3 , and so on. The SI unit is the

liter, L, which is 1000 cm 3 . A quart is 0.946 L; a U.S.

liquid gallon (gal) is 3.785 L. A barrel of petroleum 60

(U.S.) is 42 gal, or 159 L.

0 +273K

Mass Mass is the amount of matter in an object. Weight

is the force of gravity on an object. To illustrate the dif- ference, an astronaut in space has no weight but still has mass. On Earth, the two terms are directly proportional and often used interchangeably. The SI unit of mass is the kilogram, kg, which is based on a standard platinum

A-2 APPENDIX A

Energy Energy is a measure of work or heat, which used in measuring food energy is the kilocalorie, kcal, were once thought to be different quantities. Hence, two

which is 1000 cal. When Calorie is spelled with a capi- different sets of units were adopted and still persist, al-

tal C, it means kcal. If a cookbook says that a jelly though we now know that work and heat are both forms

doughnut has 185 calories, that is an error—it should say of energy.

185 Calories (capital C), or 185 kcal. A value of 185 The SI unit of energy is the joule, J, the work re-

calories (small c) would be the energy in about one quar- quired to exert a force of 1 newton through a distance of

ter of a thin slice of cucumber.

1 m. In turn, a newton is the force that gives a mass of The unit of energy in the British system is the British

thermal unit, or Btu, which is the energy needed to is not much—it is about the amount of work required to

1 kg an acceleration of 1 m/sec 2 . In human terms, a joule

warm 1 lb of water 1°F.

lift a 100-g weight to a height of 1 m. Therefore, joule units are too small for discussions of machines, power

1 Btu ⫽ 1054 J ⫽ 1.054 kJ ⫽ 252 cal plants, or energy policy. Larger units are The unit often referred to in discussions of national en-

ergy policies is the quad, which is 1 quadrillion Btu, or person)

megajoule, MJ ⫽ 10 6 J (a day’s work by one

10 15 Btu.

Some approximate energy values are gasoline)

gigajoule, GJ ⫽ 10 9 J (energy in half a tank of

1 barrel (42 gal) of petroleum ⫽ 5900 MJ The energy unit used for heat is the calorie, cal, 1 ton of coal ⫽ 29,000 MJ 1 quad ⫽ 170 million barrels of oil, or 34

which is exactly 4.184 J. One calorie is just enough en- million tons of coal ergy to warm 1 g of water 1ºC. The more common unit

APPENDIX A

A-3

II PREFIXES FOR USE WITH BASIC UNITS OF THE METRIC SYSTEM PREFIX

EQUIVALENT geo*

* Not an official SI prefix but commonly used to describe very large quantities such as the mass of water in the oceans. † The SI rules specify that SI symbols are not followed by periods, nor are they changed in the plural. Thus, it is

correct to write “The tree is 10 m high,” not “10 m. high” or “10 ms high.”

III HANDY CONVERSION FACTORS TO CONVERT FROM

MULTIPLY BY

Centimeters

Feet

0.0328 ft/cm

Inches

0.394 in/cm

Meters

0.01 m/cm

(exactly)

Micrometers (Microns)1000 ␮m/cm

Miles (statute)6.214 ⫻ 10 ⫺6 mi/cm Millimeters

(exactly) Feet

10 mm/cm

Centimeters

30.48 cm/ft

(exactly)

Inches

12 in/ft

Meters

0.3048 m/ft

Miles (statute)0.000189 mi/ft

Grams

Kilograms

0.01 kg/g

Ounces (avdp.)0.03527 oz/g Pounds (avdp.)0.002205 lb/g

Hectares

Acres

2.47 acres/ha

Inches

Centimeters

2.54 cm/in

(exactly)

Feet

0.0833 ft/in

Meters

0.0254 m/in

(exactly)

Yards

0.0278 yd/in

Kilograms

Ounces (avdp.)35.27 oz/kg Pounds (avdp.)2.205 lb/kg

Kilometers

Miles

0.6214 mi/km

Meters

Centimeters

100 cm/m

(exactly)

Feet

3.2808 ft/m

Inches

39.37 in/m

Kilometers

0.001 km/m

(exactly)

Miles (statute)0.0006214 mi/m Millimeters

1000 mm/m

(exactly)

Yards

1.0936 yd/m

A-4 APPENDIX A

III HANDY CONVERSION FACTORS (CONTINUED) TO CONVERT FROM

MULTIPLY BY

Miles (statute)Centimeters

160934 cm/mi

Feet

5280 ft/mi

(exactly)

Inches

63360 in/mi

(exactly)

Kilometers

1.609 km/mi

Meters

1609 m/mi

(exactly) Ounces (avdp.)Grams

Yards

1760 yd/mi

28.35 g/oz

(exactly) Pounds (avdp.)Grams

Pounds (avdp.)0.0625 lb/oz

453.6 g/lb

Kilograms

0.454 kg/lb

Ounces (avdp.)16 oz/lb

(exactly)

IV EXPONENTIAL OR SCIENTIFIC NOTATION tial expression. Thus, the decimal place of the number 1,000,000 is six places to the right of 1:

Exponential or scientific notation is used by scientists all over the world. This system is based on expo- nents of 10, which are shorthand notations for repeated

1 000 000 ⫽ 10 6 multiplications or divisions.

6 places

A positive exponent is a symbol for a number that is to be multiplied by itself a given number of times. Thus,

Similarly, the decimal place of the number 0.000001 the number 10 (read “ten squared” or “ten to the second

APPENDIX A Systems of Measurement