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hendricks_beginning_algebra_1e_ch1_3

Section 1.1 The Set of Real Numbers 11 1. Real numbers consist of rational numbers and irrational numbers. Rational numbers are made up of numbers that can be written as the ratio of two integers. All of the integers are elements of the set of rational numbers. The integers are positive and negative whole numbers. Whole numbers are the natural numbers combined with zero. The natural numbers are counting numbers. 2. Every real number can be graphed on a real number line. 3. For any two numbers a and b, a = b, a < b, or a > b. To determine the order of numbers, place them on the number line. The number to the right is the larger number. 4. The numbers a and -a are opposites of one another. These numbers have the same distance from zero and are on opposite sides of zero. 5. The absolute value of a number measures the number’s distance from zero on the real number line. The absolute value of a number is always zero or positive. Vertical bars, u u, denote absolute value. GRAPHING CALCULATOR SKILLS There are three basic skills that the calculator can be applied to in this section: approximating an irrational number, finding the opposite of a number, and finding the absolute value of a number. The keystrokes correspond to a TI-83 Plus or TI-84 Plus. Similar keystrokes can be used with other calculators as well. 1. Approximate the values of 13 and π. Solution: Enter the expressions on the calculator. 2nd x2 3 ) ENTER 2nd ENTER So, 13 ≈ 1.73 and π ≈ 3.14. 2. Find the opposite of -6. Solution: The symbol (-) denotes the opposite of a number and is also used to enter a negative number. So, we must use it twice to find the opposite of -6. (–) ( (–) 6 ) ENTER So, -(-6) = 6. 3. Determine the values of u-5u and -u-7u. Solution: The absolute value operation is found under the MATH menu. Press the MATH menu and then arrow right to go to the NUM menu. The first option is abs, which denotes absolute value. MATH 1 (–) 5 ) ENTER (–) MATH 1 (–) ) 7 ENTER So, u-5u = 5 and -u-7u =-7. �� ���������������� �������� EXERCISE SET Write About It! Use complete sentences to explain the meaning of each term or phrase. 1. Rational number 2. Irrational number 3. The opposite of a number 4. The absolute value of a number Determine if the statement is true or false. If a statement is false, provide an example that contradicts the statement. 5. Every rational number is also an integer. 6. All real numbers can be classified as either a rational number or an irrational number. SUMMARY OF KEY CONCEPTS


hendricks_beginning_algebra_1e_ch1_3
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