Troubleshooting Common Errors Some common errors associated with the objectives in this section are shown next. �� ������������������������ ���������������� A problem and an incorrect solution are given. Provide the correct solution and an explanation of the error. 6a. Classify the number 149. �������������������������������������� ���������������������������������������������������������������� 149 = 7 = 7 1 , so this number is a rational number, an integer, a whole number, and a natural number. 149 is an irrational number since it is a square root. The square root of a number is irrational only if the number has a decimal value that is nonrepeating and nonterminating. 6b. Plot the number 3 4 on a real number line. �������������������������������������� ���������������������������������������������������������������� 3 4 = 0.75 So, the plot of the point is between 0 and 1. –2 –1 0 1 2 3 4 5 –2 –1 0 1 2 3 4 5 6c. Simplify -u-10u. �������������������������������������� ���������������������������������������������������������������� This problem means to find the opposite of the absolute value of -10. So, we first find the absolute value of -10 and then take its opposite. - u-10u = 10 -u-10u =-(10)=-10 Objective 6 ▶ Troubleshoot common errors. 9 num e it is a square root 0u 0 ANSWERS TO STUDENT CHECKS Student Check 1 a. 0.4 = 4 10 rational, real b. -6 4 7 =- 46 7 rational, real c. 136 = 6 = 6 1 rational, integer, whole, natural, real d. 10 = 10 1 rational, integer, whole, natural, real e. 121 ≈ 4.58 irrational, real f. 5 6 rational, real g. -5 = -5 1 integer, rational, real h. 1.232232223 . . . irrational, real Student Check 2 –5.2 – –1 114 3 √⎯24 52 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 Student Check 3 a. -5 < -4 b. 12 > 1 2 c. 1.25 = 5 4 Student Check 4 a. -(-7) = 7 b. -(4) = -4 c. -a1 2 b =- 1 2 d. -a- 25 6 b = 25 6 e. -Q16R =-16 f. -(8.2) = -8.2 Student Check 5 a. 10 b. 6 c. π d. 2 5 e. -4 f. -7 10 Chapter 1 Real Numbers and Algebraic Expressions
hendricks_beginning_algebra_1e_ch1_3
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