A number written in scientific notation is written as the product of a number between 1 and 10 and a number that is a power of 10 That is, it is written as a quantity whose coefficient is between 1 and 10 and whose base is 10.
This chapter focuses on operations with numbers in scientific notation--addition, subtraction, multiplication, and division. Since a number in scientific notation is merely a certain kind of quantity with an exponent, the properties of quantities with exponents learned in the previous chapter dictate how to perform these four operations.
The first section deals with addition and subtraction. It lays out steps for adding or subtracting numbers in scientific notation, and explains why these steps make mathematical sense. The steps are derived from properties learned in Adding Exponents and Multiplying Exponents. After explaining the steps, this section provided examples of addition and subtraction.
The second section deals with multiplication and division. Like the previous section, it provides steps for multiplying and dividing numbers in scientific notation. The steps are direct results of the properties learned in Multiplying Exponents and Dividing Exponents. This section also provides examples of multiplication and division.
Scientific notation is used when dealing with very large or very small numbers. Since mathematicians, chemists, and physicists often perform operations with very large or very small numbers, it is necessary to know how to add, subtract, multiply, and divide numbers in scientific notation.
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