Operations with Scientific Notation

The arithmetic operations performed with ordinary numbers can be done with numbers written in scientific notation. However, the exponential portion of the numbers must also be considered. 

Before numbers in scientific notation can be added or subtracted, the exponents must be equal. Remember that the decimal is moved to the left to increase the exponent and to the right to decrease the exponent. 

When numbers in scientific notation are multiplied, only the decimal portion is multiplied. The exponents are added. 

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FOR PRACTICE Mathematical Operations with Scientific Notation... 

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) ... 

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... 

Chemistry is full of calculations. Our basic goal is to help you develop the knowledge and strategies you need to solve these problems. In this chapter, you will review the Metric system and basic problem solving techniques, such as the Unit Conversion Method. Your textbook or instructor may call this problem solving method by a different name, such as the Factor-Label Method and Dimensional Analysis. Check with your instructor or textbook as to for which SI (Metric) prefixes and SI-English relationships will you be responsible. Finally, be familiar with the operation of your calculator. (A scientific calculator will be the best for chemistry purposes.) Be sure that you can correctly enter a number in scientific notation. It would also help if you set your calculator to display in scientific notation. Refer to your calculator s manual for information about your specific brand and model. Chemistry is not a spectator sport, so you will need to Practice, Practice, Practice. 

In practice, we perform mathematical operations on numbers in scientific notation according to the simple rules that follow. It is not necessary to know these rules when calculations are done with a calculator (you need only know how to enter numbers), but many calculations are so simple that no calculator is needed, and you should be able to handle these operations when your calculator is broken down or not available. The simple rules are the following. 

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

Finally, the nvalue column of the vla4.property table can be populated when possible. This column stores the numerical value of the property. Since not all values are numerical, this column may have null entries. The purpose is to enable efficient use of numerical data when appropriate, for example, to select by value, sort, apply mathematical functions, etc. The following SQL will update the nvalue column when possible with a numeric value. The tilde operator in the where selects text values that match the regular expression. The expression shown here allows integers, decimal values, and scientific notation using E or e for the exponent, for example 6.023E23. 

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

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