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| Powers of Ten and Scientific Notation |

In science, very large and very small decimal numbers are conveniently expressed in terms of powers of ten, some of which are listed below:

Using powers of ten, we can write the radius of the earth in the following way, for example:

The factor of ten raised to the sixth power is ten multiplied by itself six times, or one million, so the earth’s radius is 6.38 million meters. Alternatively, the factor of ten raised to the sixth power indicates that the decimal point in the term 6.38 is to be moved six places to the right to obtain the radius as a number without powers of ten.

For numbers less than one, negative powers of ten are used. For instance, the Bohr radius of the hydrogen atom is

The factor of ten raised to the minus eleventh power indicates that the decimal point in the term 5.29 is to be moved eleven places to the left to obtain the radius as a number without powers of ten. Numbers expressed with the aid of powers of ten are said to be in scientific notation.

Calculations that involve the multiplication and division of powers of ten are carried out as in the following examples:

The general rules for such calculations are

| (A-1)

| (A-2)

| (A-3)

where n and m are any positive or negative number.

Scientific notation is convenient because of the ease with which it can be used in calculations. Moreover, scientific notation provides a convenient way to express the significant figures in a number, as Appendix B discusses.

Copyright © 2007 John Wiley & Sons, Inc. All rights reserved.