Exponential Scientific Notation

Scientists report numbers from literally astronomical to almost infinitesimal. In order to do so conveniently, we use scientific notation, also known as standard exponential notation. Scientific notation is a form of a number with a decimal coefficient times a power of 10. The following number is in scientific notation, with its parts identified ... 

In chemistry, you frequently encounter very large and very small numbers. For example, the number of molecules in a liter of air at 20°C and normal barometric pressure is 25,000,000,000,000,000,000,000, and the distance between two hydrogen atoms in a hydrogen molecule is 0.000,000,000,074 meters. In these forms, such numbers are inconvenient to write and difficult to read. For this reason, you normally express them in scientific, or exponential, notation. Scientific calculators also use this notation. 

In general, any ambiguity concerning the number of significant figures in a measurement can be resolved by using exponential notation (often referred to as scientific notation ), discussed in Appendix 3. 

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... 

On all scientific calculators it is possible to enter numbers in exponential notation. The method used depends on the brand of calculator. Most often, it involves using a key labeled [exp), [ ee 1, or [eex]. Check your instruction manual for the procedure to be followed. To make sure you understand it, try entering the following numbers ... 

Another way to determine the number of significant figures in a number is to express it in scientific (exponential) notation. The number of digits shown is the number of significant figures. For example, 2.305 X 10 5 would contain four significant figures. 

Discover howto deal with, organize, and use all the numbers that play a huge role in chemistry. In particular, find out about exponential and scientific notation as well as precision and accuracy. 

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

Usin0 Exponential and Scientific Notation to Report Measurements... 

To make working with such extreme numbers easier, chemists turn to scientific notation, which is a special kind of exponential notation. Exponential notation simply means writing a number in a way that includes exponents. In scientific notation, every number is written as the product of two numbers, a coefficient and a power of 10. In plain old exponential notation, a coefficient can be any value of a number multiplied by a power with a base of 10 (such as 10" ). But scientists have rules for coefficients in scientific notation. In scientific notation, the coefficient is always at least 1 and always less than 10. For example, the coefficient could be 7, 3.48, or 6.0001. 

A major benefit of presenting numbers in scientific notation is that it simplifies common arithmetic operations. The simplifying abilities of scientific notation cire most evident in multiplication and division. (As we note in the next section, addition and subtraction benefit from exponential notation but not necesscirily from strict scientific notation.)... 

Addition or subtraction gets easier when you express your numbers as coefficients of identical powers of 10. To wrestle your numbers into this form, you may need to use coefficients less than 1 or greater than 10. So scientific notation is a bit too strict for addition and subtraction, but exponential notation still serves you well. 

Be a good chemist. Report your measurements in scientific notation to avoid such annoying ambiguities. (See the earlier section Using Exponential and Scientific Notation to Report Measurements for details on scientific notation.)... 

Many of the numbers you will deal with will either be very large (e.g., Avogadro s number— 6.02 X 1023) or very small (e.g., Planck s constant—6.63 X 10 34 J s). Rather than write these numbers with all of the zeros, it is much easier to use scientific (or exponential) notation ... 

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)... 

In using such large and small numbers, it is inconvenient to write down all the zeroes. In scientific (exponential) notation, we place one nonzero digit to the left of the decimal. 

In chemistry we frequently use very large or very small numbers. Such numbers are conveniently expressed in scientific, or exponential, notation. 

It is often difficult to express very large numbers to the proper number of significant figures using conventional notation. The solution to this problem lies in the use of scientific notation, also referred to as exponential notation, which involves the representation of a number as a power of ten. 

Chapter 1 describes the use of scientific notation (exponential notation) to represent such numbers more conveniently. The rules for scientific notation, as summarized there, are as follows ... 

Exponential (scientific) notation provides a much more practical way of writing such numbers. In exponential notation, we express numbers in the form... 

Ans. When numbers in exponential or scientific notation are multiplied, the coefficients are multiplied and the exponents are added ... 

Express each of the following numbers in scientific (exponential) notation. 

Many scientific calculators have a key labeled EXP or EE, which is used to enter numbers in exponential notation. To enter the number 5.8 X 10 on such a calculator, the key sequence is... 

Scientific calculators are generally able to convert numbers to exponential notation using one or two keystrokes frequently SCI for scientific notation will convert a number into exponential notation. Consult your instruction manual to see how this operation is accomplished on your calculator. 

The prefixes in Table 2.4 are represented by the powers of 10 used in scientific, or exponential, notation for writing large and small numbers. For example, 10 = 10 X 10 X 10 = 1000. Appendix B reviews this notation. 

What are the results for the following operations in exponential notation You may need to refer to Appendix B on scientific notation for questions 46 and 47. 

Scientific notation, also known as exponential notation, is a way of representing large and small numbers as the product of two terms. The first term, the coefficient, is a number between 1 and 10. The second term, the exponential term, is 10 raised to a power—the exponent. For example. 

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