The Foundations of Chemistry

USE OF NUMBERS

In chemistry, we measure and calculate many things, so we must be sure we understand

how to use numbers. In this section we discuss two aspects of the use of numbers: (1) the

notation of very large and very small numbers and (2) an indication of how well we

actually know the numbers we are using. You will carry out many calculations with cal-

culators. Please refer to Appendix A for some instructions about the use of electronic

calculators.

Scientific Notation

We use scientific notationwhen we deal with very large and very small numbers. For

example, 197 grams of gold contains approximately

602,000,000,000,000,000,000,000 gold atoms

The mass of one gold atom is approximately

0.000 000 000 000 000 000 000 327 gram

In using such large and small numbers, it is inconvenient to write down all the zeroes. In

scientific (exponential) notation, we place one nonzero digit to the left of the decimal.

4,300,000.
4.3 106

6 places to the left, exponent of 10 is 6

0.000348
3.48 10 ^4

4 places to the right, exponent of 10 is  4

The reverse process converts numbers from exponential to decimal form. See Appendix

A for more detail, if necessary.

1-

In exponential form, these numbers
are

6.02 1023 gold atoms

3.27 10 ^22 gram

20 CHAPTER 1: The Foundations of Chemistry

Problem-Solving Tip:Know How to Use Your Calculator

Students sometimes make mistakes when they try to enter numbers into their calcula-

tors in scientific notation. Suppose you want to enter the number 4.36 10 ^2. On most

calculators, you would

(1) press 4.

(2) press EE or EXP, which stands for “times ten to the”

(3) press 2 (the magnitude of the exponent) and thenor CHS (to change its sign)

The calculator display might show the value as 4.36 02 or as 0.0436. Different

calculators show different numbers of digits, which can sometimes be adjusted.

If you wished to enter 4.36 102 , you would

(1) press 4.36, then pressor CHS to change its sign,

(2) press EE or EXP, and then press 2

The calculator would then show 4.36 02 or 436..

See the Saunders Interactive
General Chemistry CD-ROM,
Screen 1.17, Using Numerical
Information.