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I* Chapter 1 Matter, Energy, and Measurement

answer cannot be good to three decimal places. As a scientist, it is important to report data that have the correct number of significant figures. A de- tailed account of using signifrcant figures is presented in Appendix II. The following How To box describes the way to determine the number of signifi- cant figures in a number. You will find boxes like this at places in the text where detailed explanations ofconcepts are useful.

HowTo... Determine the Number of Significant Figures in a Number 1. Nonzero digits are always significant.

For example ,233.'l- m has four significant figures;2.3 g has two significant figures.

2. Zeros at the beginning of a number are never significant. For example, 0.0055 L has two signifieant figures; 0.3456 g has four significant figures.

S-.Zeros between nouzero digits are always significant. For example,2.045 kcal has four significant figures; 8.0506 g has five significant figures.

4. Ziros at the end of a number that contains a decimal point are always significant For exampie, 3.00 L has three significant figures; 0.0450 mm has three significant figures.

5. Zeros at the end of a number that contains no decimal point may or may not be significant.

We cannot tell whether they are significant without knowing something about the number. This is the ambiguous case. If you know that a certain small business made a profit'of $36,000 last year, you can be sure that the 3 and 6 are sigaifieant, but what about the reet? The profit might have been $36,126 or $35,786.53, or maybe even exactly $36,000. We just don't know because it is customary to round offsuch numbers. On the

, other hand, if the profit were reported as $36,000.00, then all seven figits' would be significant.

Jn seience, to get around the ambiguous case, we use exponential notation. Suppose a measuremeat eomes out to be 2500 g. If we made the measurement, then we know whether the two zeros are signifieant, but we need to tell others. If these digits are not significant, we uriite our number as 2.5 x 103. If one zer,o is sigrrificant, we write 2.50 x L03. If both zeros are significant, we write 2.500 x 103. Because *e now have a decimal point, all'the digits'shown are sigpifcant. We are going to use decimal points throughout-this text to indieate tJre number of significant figures.

Multiply: " (a) @.73 x 105X1.37 x 102) Divide:

7.08 x 10-8(c)-' 300.

(b) (2.7 x 10-4X5.9 x 108)

5.8x106(d) ^6.6x10o

7.05 x 10 3(e) - 4.51 x 10',

Use your calculator for this example.