Appendix A

Measurement and Units

Table A.1

Common Units and Their Abbreviations
Note that the abbreviation for inch (in.) is the only abbreviation that ends in a period.

Type of
measurement

Unit

Abbreviation

English mass

ton

ton

pound

lb

ounce

oz

English length

mile

mi or mile

yard

yd

foot

ft

inch

in.

English volume

gallon

gal

quart

qt

pint

pt

fluid ounce

fl oz

cubic foot

cu ft

cubic inch

cu in.

Time

year

yr or year

day

d or day

hour

h or hr

minute

min

second

s or sec

Temperature

degree Celsius

°C

degree Fahrenheit

°F

kelvin

K

Energy

joule

J

calorie

cal

dietary calorie

Cal

Table A.2

English-English Conversion Factors

Type of
measurement

Conversion Factors

Length

Mass

Volume

Table A.3

The Relationship Between English and Metric Length Units

Both four and eight digits are given for each relationship. Four digits will be used for nearly all of the English-metric conversions done in this text.

Metric length

English length

kilometer (km)

0.6214 mi or 0.62137119 mi

3281 ft or 3280.8399 ft

meter (m)

3.281 ft or 3.2808399 ft

39.37 in. or 39.370079 in.

1.094 yd or 1.0936133 yd

centimeter (cm)

0.3937 in. or 0.39370079 in.

0.03281 ft or 0.032808399 ft

millimeter (mm)

3.937 × 10⁻² in.

   or 3.9370079 × 10⁻² in.

micrometer (μm)

3.937 × 10⁻⁵ in.

   or 3.9370079 × 10⁻⁵ in.

nanometer (nm)

3.937 × 10⁻⁸ in.

   or 3.9370079 × 10⁻⁸ in.

English length

Metric length

mile (mi)

1.609 km or 1.609344 km (exact)

1609 m or 1609.344 m (exact)

yard (yd)

0.9144 m (exact)

   or 91.44 cm (exact)

foot (ft)

30.48 cm (exact)

   or 0.3048 m (exact)

inch (in.)

2.54 cm (exact)

   or 0.0254 m (exact)

Table A.4

The Relationship Between English and Metric Mass Units

Both four and eight digits are given for each relationship. Four digits will be used for nearly all of the English-metric conversions done in this text.

Metric Mass

English Mass

metric ton (t)

1.102 ton (short)
   or 1.1023113 ton (short)

2205 lb or 2204.6226 lb

kilogram (kg)

2.205 lb or 2.2046226 lb

0.001102 ton
   or 0.0011023113 ton

gram (g)

0.002205 lb
   or 0.0022046226 lb

0.03527 oz
   or 0.035273962 oz

milligram (mg)

3.527 × 10⁻⁵ oz
   or 3.5273962 × 10⁻⁵ oz

microgram (μg)

3.527 × 10⁻⁸ oz
   or 3.5273962 × 10⁻⁸ oz

English Mass

Metric Mass

ton (ton)

0.9072 metric tons

   or 0.90718474 metric tons

907.2 kg or 907.18474 kg

pound (lb)

453.6 g or 453.59237 g

0.4536 kg or 0.45359237 kg

ounce (oz)

28.35 g or 28.349523 g

2.835 × 10⁴ mg

   or 2.8349523 × 10⁴ mg

Table A.5

The Relationship Between English and Metric Volume Units

Both four and eight digits are given for each relationship. Four digits will be used for nearly all of the English-metric conversions done in this text.

Metric volume

English volume

liter (L)

1.057 qt or 1.056718 qt

0.2642 gal or 0.2641795 gal

33.81 fl oz or 33.81498 fl oz

61.03 cu in. or 61.02545 cu in.

milliliter (mL)

0.03381 fl oz or 0.03381497 fl oz

0.06103 cu in. or 0.06102545 cu in.

microliter (μL)

3.381 × 10⁻⁵ fl oz

   or 3.381497 × 10⁻⁵ fl oz

cubic centimeter (cm³)

0.03381 fl oz or 0.03381497 fl oz

0.06103 cu in. or 0.06102545 cu in.

English volume

Metric volume

gallon* (gal)

3.785 L or 3.785306 L

3785 mL or 3785.306 mL

quart* (qt)

0.9463 L or 0.9463264 L

946.3 mL or 946.3264 mL

fluid ounce* (fl oz)

0.02957 L or 0.02957270 L

29.57 mL or 29.57270 mL

cubic inch (cu in.)

16.39 cm³

   or 16.387064 cm³ (exact)

16.39 mL

   or 16.387064 mL (exact)

0.1634 L

   or 0.16387064 L (exact)

* There are three kinds of gallons, quarts, and fluid ounces: British, U.S. dry, and U.S. liquid. The values given here are for U.S. liquid gallons, quarts, and fluid ounces.

Appendix B

Scientific Notation

Numbers expressed in scientific notation have the following form:

For example, there are about 5.5 × 10²¹ carbon atoms in a 0.55 carat diamond. In the number 5.5 × 10²¹, 5.5 is the coefficient, 10²¹ is the exponential term, and 21 is the exponent. The coefficient, which should have just one nonzero digit to the left of the decimal point, reflects the number’s uncertainty. It is common to assume that numbers are plus or minus one in the last position reported unless otherwise stated. Using this guideline, 5.5 × 10²¹ carbon atoms in a 0.55 carat diamond suggests that there are from 5.4 × 10²¹ to 5.6 × 10²¹ carbon atoms in the stone.

The exponential term shows the size of the number. Positive exponents are used for large numbers, and negative exponents are used for small numbers. For example, the moon orbits the sun at 2.2 × 10⁴ or 22,000 mi/hr.

2.2 × 10⁴ = 2.2 × 10 × 10 × 10 × 10 = 22,000

A red blood cell has a diameter of about 5.6 × 10⁻⁴ or 0.00056 inches.

Use the following steps to convert from a decimal number to scientific notation.

Shift the decimal point until there is one nonzero number to the left of the decimal point, counting the number of positions the decimal point moves.

Write the resulting coefficient times an exponential term in which the exponent is positive if the decimal point was moved to the left and negative if the decimal position was moved to the right. The number in the exponent is equal to the number of positions the decimal point was shifted.

For example, when 22,000 is converted to scientific notation, the decimal point is shifted four positions to the left so the exponential term has an exponent of 4.

When 0.00056 is converted to scientific notation, the decimal point is shifted four positions to the right so the exponential term has an exponent of -4.

To convert from scientific notation to a decimal number, shift the decimal point in the coefficient to the right if the exponent is positive and to the left if it is negative. The number in the exponent tells you the number of positions to shift the decimal point. For example, when 2.2 × 10⁴ is converted to a decimal number, the decimal point is shifted four positions to the right because the exponent is 4.

2.2 × 10⁴ goes to 22,000

When 5.6 × 10⁻⁴ is converted to a decimal number, the decimal point is shifted four positions to the left because the exponent is -4.

5.6 × 10⁻⁴ goes to 0.00056

There are two reasons for using scientific notation. The first is for convenience. It takes a lot less time and space to report the mass of an electron as 9.1096 × 10⁻²⁸, rather than 0.00000000000000000000000000091096 g. The second reason is to more clearly report the uncertainty of a value. For example, a typical peanut butter sandwich provides our bodies about 1.4 × 10³ kJ of energy. Because of the variation in the type and amount of peanut butter added to the sandwich, there’s some variation in the energy provided. The value 1.4 × 10³ kJ suggests that the energy from a typical peanut butter sandwich could range from 1.3 × 10³ kJ to 1.5 × 10³ kJ. If the value is reported as 1400 kJ, its uncertainty would not be so clear. It could be 1400 ± 1, 1400 ± 10, or 1400 ± 100.

When multiplying exponential terms, add exponents.

10³ • 10⁶ = 10³⁺⁶ = 10⁹

10³ • 10⁻⁶ = 10³⁺⁽⁻⁶⁾ = 10⁻³

3.2 × 10⁻⁴ • 1.5 × 10⁹ = 3.2 • 1.5 • 10⁻⁴⁺⁹ = 4.8 × 10⁵

When dividing exponential terms, subtract exponents.

When raising exponential terms to a power, multiply exponents.

(10⁴)³ = 104•3 = 10¹²

(3 × 10⁵)² = (3)² • (10⁵)² = 9 × 10¹⁰