The Solar System

APPENDIX A 605

Very small numbers can also be written with powers of 10.

For example, the wavelength of visible light is about 0.0000005

m. In powers of 10 this becomes 5  10 −7 m.

Th e powers of 10 used in this notation appear below. Th e

exponent tells you how to move the decimal point. If the exponent

is positive, move the decimal point to the right. If the exponent

is negative, move the decimal point to the left. For example,

2.0000  103 equals 2000, and 2  10 −3 equals 0.002.

105  100,000

104  10,000

103  1,000

102  100

101  10

100  1

10 ^1  0.1

10 ^2  0.01

10 ^3  0.001

10 ^4  0.0001

If you use scientifi c notation in calculations, be sure you

correctly enter the numbers into your calculator. Not all calcula-

tors accept scientifi c notation, but those that can have a key

labeled EXP, EEX, or perhaps EE that allows you to enter the

exponent of ten. To enter a number such as 3  108 , press the

keys 3 EXP 8. To enter a number with a negative exponent, you

must use the change-sign key, usually labeled / or CHS. To

enter the number 5.2  10 −3, press the keys 5.2 EXP / 3. Try

a few examples.

To read a number in scientifi c notation from a calculator

you must read the exponent separately. Th e number 3.1  1025

may appear in a calculator display as 3.1 25 or on some calcula-

tors as 3.1 10^25. Examine your calculator to determine how such

numbers are displayed.

Example: Th e radius of the moon is 1738 km. What is this in
miles? Table A-3 indicates that 1.000 mile equals 1.609 km, so

1738 km  (1.000 mi)

(1.609 km)

 1080 mi

Temperature Scales

In astronomy, as in most other sciences, temperatures are
expressed on the Kelvin scale, although the centigrade (or
Celsius) scale is also used. Th e Fahrenheit scale commonly used
in the United States is not used in scientifi c work.
Temperatures on the Kelvin scale are measured from abso-
lute zero, the temperature of an object that contains no extract-
able heat. In practice, no object can be as cold as absolute zero,
although laboratory apparatuses have reached temperatures lower
than 10−6 K. Th e Kelvin scale is named after the Scottish
mathematical physicist William Th omson, Lord Kelvin
(1824–1907).
Th e centigrade scale refers temperatures to the freezing point
of water (0°C) and to the boiling point of water (100°C). One
degree centigrade is ____ 1001 of the temperature diff erence between
the freezing and boiling points of water, thus the prefi x centi. Th e
centigrade scale is also called the Celsius scale after its inventor,
the Swedish astronomer Anders Celsius (1701–1744).
Th e Fahrenheit scale fi xes the freezing point of water at 32°F
and the boiling point at 212°F. Named after the German physi-
cist Gabriel Daniel Fahrenheit (1686–1736), who made the fi rst
successful mercury thermometer in 1720, the Fahrenheit scale is
used routinely only in the United States.
It is easy to convert temperatures from one scale to another
using the information given in ■ Table A-4.

Powers of 10 Notation

Powers of 10 make writing very large numbers much simpler. For
example, the nearest star is about 43,000,000,000,000 km from
the sun. Writing this number as 4.3  1013 km is much easier.

Example: Th e radius of the moon is 1738 km. What is this in

■ Table A-3 ❙ Conversion Factors

Between British and Metric Units

1 inch  2.54 centimeters 1 meter  39.36 inches  3.28 feet

1 foot  0.3048 meter 1 kilometer  0.6214 mile

1 mile  1.609 kilometers 1 kilogram  0.0685 slug

1 slug  14.59 kilograms 1 Newton  0.2248 pound

1 pound  4.448 Newtons 1 Joule  0.7376 foot-pound

1 foot-pound  1.356 Joules 1 Joule/s  0.001341 horsepower

1 horsepower  745.7 Joules/s 1 Joule/s  1 Watt

1 centimeter  0.394 inch

■ Table A-4 Temperature Scales and

Conversion Formulas

Kelvin

(K)

Centigrade

(°C)

Fahrenheit

(°F)

Absolute zero 0 K 273°C 459°F

Freezing point of water 273 K 0°C 32°F

Boiling point of water 373 K 100°C 212°F

Conversions:

K  °C + 273

°C  (^59 )(°F − 32)

°F  (^95 )(°C) + 32