With scientific notation

You can use these laws of exponents with scientific notation. 

X10 The ease of math with scientific notation shines through in this problem. Dividing the coefficients yields a coefficient quotient of 9.3/3.1 =3.0, and dividing the powers of ten (by subtracting their exponents) yields a quotient of 10 /10 = 10" " = 10 . Marrying the two quotients produces the given answer, already in scientific notation. 

Chemists routinely measure quantities that run the gamut from very small (the size of an atom, for example) to extremely large (such as the number of particles in one mole). Nobody, not even chemists, likes dealing with scientific notation (which we cover in Chapter 1) if they don t have to. For these reasons, chemists often use a metric system prefix (a word part that goes in front of the base unit to indicate a numerical value) in lieu of scientific notation. For example, the size of the nucleus of an atom is roughly 1 nanometer across, which is a nicer way of saying 1x10- meters across. The most useful of these prefixes are in Table 2-2. 

Notice how numbers that are either very large or very small are indicated in Table 1.4 using an exponential format called scientific notation. For example, the number 55,000 is written in scientific notation as 5.5 X 104, and the number 0.003 20 as 3.20 X 10 3. Review Appendix A if you are uncomfortable with scientific notation or if you need to brush up on how to do mathematical manipulations on numbers with exponents. 

You will probably use your calculator for most calculations. It is critical that you learn to use the scientific notation feature of your calculator properly. Calculators vary widely, but virtually all scientific calculators have either an EE key or an EXP key that is used for scientific notation. Unfortunately, these calculators also have a 10 key, which is the antilog key and has nothing to do with scientific notation, so don t use it when entering numbers in scientific... 

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. 

Mode of operation. Calculators fall into two distinct groups. The older system used by, for example, Hewlett Packard calculators is known as the reverse Polish notation to calculate the sum of two numbers, the sequence is 2 [enter] 4 -h and the answer 6 is displayed. The more usual method of calculating this equation is as 2- -4=, which is the system used by the majority of modern calculators. Most newcomers find the latter approach to be more straightforward. Spend some time finding out how a calculator operates, e.g. does it have true algebraic logic (y then number, rather than number then -/) How does it deal with scientific notation (p. 262) ... 

Write the numbers 357 and 0.0055 in scientific notation, if you are having difficulty with scientific notation, read the Appendix. 

FOR PRACTICE Mathematical Operations with Scientific Notation... 

With scientific notation, the exponents of 10 are used to indicate the decimal place. Thus,... 

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