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

less than.

       Remember that, in any true statement, the large open mouth of the symbol is on the side of the greater amount, and the small point is on the side of the lesser amount.

      Less than or equal to (≤) and greater than or equal to (≥)

      The symbol ≤ means less than or equal to. For example, the following statements are true:

      Similarly, the symbol ≥ means greater than or equal to. For example,

       The symbols ≤ and ≥ are called inclusive inequalities because they include (allow) the possibility that both sides are equal. In contrast, the symbols < and > are called exclusive inequalities because they exclude (don’t allow) this possibility.

      Approximately equals (≈)

      In Chapter 3, I show you how rounding numbers makes large numbers easier to work with. In that chapter, I also introduce ≈, which means approximately equals.

      For example,

      You can also use ≈ when you estimate the answer to a problem:

      Q. Place the correct symbol (=, >, or <) in the blank:

      A. <. Because is less than 5, use the symbol that means is less than.

      Q. Place the correct symbol (=, >, or <) in the blank:

      A. >. Because and is greater than 20, use the symbol that means is greater than.

      Q. Sam worked 7 hours for his parents at $8 an hour, and his parents paid him with a $50 bill. Use the symbol ≠ to point out why Sam was upset.

A. Sam worked 7 hours for $8 an hour, so here’s how much he earned:

      He was upset because his parents didn’t pay him the correct amount:

      Q. Find an approximate solution to

      A. 8,000,000. The two numbers are both in the millions, so you can use ≈ to round them to the nearest million:

      Now it’s easy to add

      15 Place the correct symbol in the blanks:

      (a)

      (b)

      (c)

      (d)

      16 Change the ≠ signs to either > or <:

      (a)

      (b)

      (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