SAT Math For Dummies with Online Practice. Mark Zegarelli

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      When a decimal includes three or more decimal places, the decimal point remains in the resulting percentage. For example:

      Changing percentages to decimals

      Converting a percentage to a decimal reverses the process I describe in the previous section. To convert a percentage that doesn’t have a decimal point, introduce a decimal point just before the percent sign, then move it two places to the left and drop the percent sign. For example:

      As you can see from this example, after changing a percentage to a decimal, you can safely drop unnecessary trailing zeros.

      For percentages that are less than 10%, introduce one or more place-holding zeros as needed into the decimal that you create. For example:

Absolute Value

      The absolute value of a number is its non-negative value. For example:

      As you can see, when absolute value is applied to a negative number such as –3, the minus sign is dropped. Otherwise, absolute value has no effect on non-negative numbers such as 5 and 0.

When evaluating an absolute value, evaluate the expression inside the absolute value bars, then apply the absolute value, and then evaluate the rest of the expression. For example:

       Which of the following is equivalent to ?

      (A) –13

      (B) –7

      (C) 7

      (D) 13

      To begin, simplify the two expressions inside the absolute value bars:

      Next, substitute and :

      Now complete the problem:

      Therefore, Answer B is correct.

Radicals

      A radical (also called a root) is the inverse of an exponent — that is, a radical “undoes” an exponent. For example:

so

so

so

      The most common type of radical on the SAT is the square root. In this section, I discuss the basics of radicals.

      Understanding radicals

Radicals, such as , arise from reversing the process of squaring a number. That is, they are inverse operations. Table 2-1 shows you the results of squaring the first five positive integers and then taking the square root (radical) of the result.

TABLE 2-1 Squaring and Taking a Square Root (Radical) Are Inverse Operations

Squares	Square Roots (Radicals)