Calculator use, scientific notation

You must be able to enter numbers easily and unerringly into your calculator using scientific notation With most calculators, this would be accomplished as follows. 

Example 9.5 Stoichiometric Calculations Using Scientific Notation... 

Many scientific calculators write scientific notation using the letter E instead of a power of 10. On your calculator screen, you ll see 2.3E26 instead of 2.3 x 1026 or 1.23E-39 instead of 1.23 x 10 39. This isn t a big problem — you just want to be aware of this cryptic notation so that you know what it means and can write it correctly. 

Scientific notation provides a convenient way to write very large or very small numbers using powers of 10. You should be able to write, interpret, and perform calculations with numbers written using scientific notation. 

To simplify reporting large numbers and doing calculations, you can use scientific notation. As you learned in an earlier mathematics course, scientific notation works by using powers of 10 as multipliers. 

Some calculators display answers in decimal notation unless they are programmed to display them in scientific notation. If a number is too large or too small to fit on the display in decimal format, the calculator will use scientific notation automatically. To get a display in scientific notation for a reasonably sized decimal number, see the owner s manual. If an easy conversion is not available, multiply the decimal value by 1 X 10 ° (if the number is greater than 1) or 1 X 10 ° (if the number is less than 1), and mentally subtract or add 10 to the resulting exponent. 

Both very large and very small numbers are commonly encountered in process calculations. A convenient way to represent such numbers is to use scientific notation, in which a number is expressed as the product of another number (usually between 0.1 and 10) and a power of 10. 

Express the following calculations in the proper number of significant figures. Use scientific notation where appropriate. 

Express numbers using scientific notation, ard do calculations with numbers expressed in scientific notation. (Section 1.7)... 

Multiplication and division calculations involving scientific notation are easily done using a hand calculator, t Table 1.4 gives the steps, the typical calculator procedures (buttons to press), and typical calculator readout or display for the division of 7.2 X 10 by 1.2 X 10 . 

Numbers such as these are very awkward to work with. For example, neither of the numbers just written could be entered directly on a calculator. Operations involving very large or very small numbers can be simplified by using exponential (scientific) notation. To express a number in exponential notation, write it in the form... 

Note (2) It is more difficult to find K in scientific notation because most calculators cannot handle numbers this big. So, use what you know about exponents to solve for K ... 

Another common, but more sophisticated, representation of numbers is scientific notation. This notation minimizes the tendency to make errors in arithmetical operations it is used extensively in chemistry. It is imperative that you be completely comfortable in using it. Hand calculators will accept extremely large or extremely small numbers through the keyboard in scientific notation. Ready and proper use of this notation requires a good understanding of the following paragraphs. 

Some calculators make it possible for you to choose in advance that all results be displayed in scientific notation (or decimal notation), regardless of which notation you use for entering numbers You can also choose how many decimal places (usually up to a maximum of 8) will be displayed in decimal notation, or in the lefthand factor of scientific notation If your calculator has... 

We have discussed at length the usefulness of powers of 10 as part of scientific notation, but many practical problems involve the powers of other numbers. For example, the area of a circle involves the square of the radius, and the volume of a sphere involves the cube of the radius. Nearly every calculator yields the square of a number when you simply enter the number through the keyboard and then press the ke ihe S( uafe appears in the lighted display. 

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... 

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 next step is entering a number written in scientific notation into a calculator. Locate the EXP key. For practice, enter the frequently used chemistry number 6.02 x 1023 by performing the following steps. 

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. 

To use exponential notation to work with very large and very small numbers To use the basic elements of the metric system—a system of units and prefixes designed to make scientific calculations as easy as possible... 

Exponential notation enables easy reporting of extremely large and extremely small numbers. A number in scientific notation consists of a coefficient times 10 to an integral power, where the coefficient is equal to or greater than 1 but less than 10. Learn how to convert numbers from exponential notation to ordinary decimal values, and vice versa, and also how to use exponential numbers in calculations. Also learn to use effectively an electronic calculator with exponential capability (see Appendix 1). (Section 2.2)... 

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) ... 

Suppose you must do a calculation using the measurement 200 L. You cannot be certain which zero was estimated. To indicate the significance of digits, especially zeros, write measurements in scientific notation. In scientific notation, all digits in the decimal portion are significant. Which of the following measurements is most precise ... 

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