Scientific notation and

When you know how to express your numbers in scientific notation and how to distinguish between precision and accuracy (we cover both topics earlier in this chapter), you can bask in the glory of a new skill using scientific notation to express precision. The beauty of this system is that simply by looking at a measurement, you know just how precise that measurement is. 

Note that the characteristic is determined by the power to which 10 is raised (when the number is in standard scientific notation), and the mantissa is determined by the log of the lefthand factor (when the number is in scientific notation). It is these properties that make it so easy to find the logarithm of a number using a log table. Here is how you can do it. 

Scientific notation and decimals (integral powers and roots of base 10). 

A. Express each of the following in standard scientific notation, and also give the answer in that notation. 

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. 

The metric system is a decimal system, based on powers of 10. Table 2.5 is a list of the prefixes for the various powers of 10. Between scientific notation and the prefixes shown below, it is very simple to identify, name, read, and understand 36 decades of power of any given base or derived unit. 

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. 

XEST 1- Express the following quantities in scientific notation and indicate how many significant... 

Perform the following operation. Express the answer in scientific notation and with the correct number of significant figures. 

You will convert data into scientific notation and from one unit to another. 

A Scientific Notation and Experimental Error A.2 B SI Units, Unit Conversions, Physics for General Chemistry A.9 C Mathematics for General Chemistry A.21 D Standard Chemical Thermodynamic Properties A.37 E Standard Reaction Potentials at 25°C A.45 F Physical Properties of the Elements A.47 G Solutions to the Odd-Numbered Problems A.57... 

The key to solving this problem correctly is to remember that we are looking at numbers in scientific notation and that these numbers all have negative exponents. Some students only look at the coefficients, and try to use them to judge the size of the number. What you really need to do is convert these numbers to standard notation, and then see which is the largest. 

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. 

EXAMPLE 11 Perform the following arithmetic operations with exponential numbers, giving the answers in scientific notation and with the proper number of significant digits ... 

Report data and results using scientific notation and the proper number of significant figures. 

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