Scientific Notation with Significant Figures

Skills Toolkit 4 Scientific Notation with Significant Figures... 

In this unit you will find explanations, examples, and practice dealing with the calculations encountered in the chemistry discussed in this book. The types of calculations included here involve conversion factors, metric use, algebraic manipulations, scientific notation, and significant figures. This unit can be used by itself or be incorporated for assistance with individual units. Unless otherwise noted, all answers are rounded to the hundredth place. The calculator used here is a Casio FX-260. Any calculator that has a log (logarithm) key and an exp (exponent) key is sufficient for these chemical calculations. 

Having surveyed some of the units used in chemistry, we now turn to techniques for handling numbers associated with measurements scientific notation and significant figures. 

Crunching numbers in scientific and exponential notation Telling the difference between accuracy and precision Doing math with significant figures... 

Use your calculator to do each calculation and state the answer in scientific notation with the correct number of significant figures. 

Challenge Write the numbers 10, 100, and 1000 in scientific notation with two, three, and four significant figures, respectively. 

Write each of the following in scientific notation with two significant figures ... 

A good portion of the AP Chemistry Test deals with calculations, either with or without the aid of a calculator. For all of these problems, there are two different components—the chemistry component and the math component. Most of this book is devoted to a review of the chemistry component of the problems, but this chapter is designed to review a few important mathematical skills that you will need to know as you work through the problems. Three skills that are critical to success on the AP Chemistry Test use significant figures, scientific notation, and dimensional analysis. 

Initial zeros are not significant. For example, in 0.0203 the first two zeros can be replaced with scientific notation and the number can be written as 2.03 x 10-2. This example has only three significant figures. 

Step 8 Calculate your answer and report it with the correct significant figures (in scientific notation, if necessary) and with the correct unit. 

Very large and very small numbers may be represented with the proper number of significant figures by using scientific notation. 

Two undefined numbers expressed in regular notation are shown below, along with the number of places the decimal must move to express each in scientific notation. If each X represents a significant figure, write each number in scientific notation. 

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