Basic Math & Pre-Algebra All-in-One For Dummies (+ Chapter Quizzes Online). Mark Zegarelli

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      (c)

      (d)

      17 Tim’s boss paid him for 40 hours of work last week. Tim accounted for his time by saying that he spent 19 hours with clients, 11 hours driving, and 7 hours doing paperwork. Use ≠ to show why Tim’s boss was unhappy with Tim’s work.

      18 Find an approximate solution to 10,002 − 6,007.

Moving Beyond the Big Four: Exponents and Square Roots

      In this section, I introduce you to three new operations that you need as you move on with math: exponents, square roots, and absolute value. As with the Big Four operations, these three operations tweak numbers in various ways.

To tell the truth, these three operations have fewer everyday applications than the Big Four. But you’ll be seeing a lot more of them as you progress in your study of math. Fortunately, they aren’t difficult, so this is a good time to become familiar with them.

      Understanding exponents

      Exponents (also called powers) are shorthand for repeated multiplication. For example, means to multiply 2 by itself three times. To do that, use the following notation:

      In this example, 2 is the base number and 3 is the exponent. You can read as “2 to the third power” or “2 to the power of 3” (or even “2 cubed,” which has to do with the formula for finding the volume of a cube — see Chapter 19 for details).

      Here’s another example:

      That works out like this:

      This time, 10 is the base number and 5 is the exponent. Read as “10 to the fifth power” or “10 to the power of 5.”

       When the base number is 10, figuring out any exponent is easy. Just write down a 1 and that many 0s after it:

1 with two 0s	1 with seven 0s	1 with twenty 0s

      Exponents with a base number of 10 are important in scientific notation, which I cover in Chapter 17.

      The most common exponent is the number 2. When you take any whole number to the power of 2, the result is a square number. (For more information on square numbers, see Chapter 1.) For this reason, taking a number to the power of 2 is called squaring that number. You can read as “three squared,” as “four squared,” and so forth. Here are some squared numbers:

       Any number (except 0) raised to the 0 power equals 1. So are equivalent, or equal, because they all equal 1.

      Discovering your roots

      Earlier in this chapter, in the section, “Switching Things Up with Inverse Operations and the Commutative Property,” I show you how addition and subtraction are inverse operations. I also show you how multiplication and division are inverse operations. In a similar way, roots are the inverse operation of exponents.

      The most common root is the square root. A square root undoes an exponent of 2. For example,

      You can read the symbol either as “the square root of” or as “radical.” So read as either “the square root of 9” or “radical 9.”

      As you can see, when you take the square root of any square number, the result is the number that you multiplied by itself to get that square number in the first place. For example, to find , you ask the question, “What number when multiplied by itself equals 100?” The answer here is 10 because

      You probably won’t use square roots much until you get to algebra, but at that point, they become handy.

      Q. What is 3⁴?

      A. 81. The expression tells you to multiply 3 by itself 4 times:

      Q. What is ?

      A. 1,000,000. Using the power of ten rule, is 1 followed by six 0s, so СКАЧАТЬ