NAME _____________________________________________ DATE ____________________________ PERIOD ____________ Notes: 1-1 The Real Number System Numbers may be classified by identifying to which of the following sets they belong. Natural Numbers Numbers used for counting. {1, 2, 3, 4, 5, …} Whole Numbers The set of natural numbers and 0. {0, 1, 2, 3, 4, …} Integers The set of whole numbers and their opposites {…, –2, –1, 0, 1, 2, …} a Rational Numbers Numbers that can be expressed in the form , where a and b are integers and b ≠ 0. b a Irrational Numbers Numbers that cannot be expressed in the form , where a and b are integers and b ≠ 0. b Classify each number by determining all sets of numbers to which it belongs. a. 5 b. 0.666… c. –√25 d. –√11 Classify each number by determining all sets of numbers to which it belongs. Then write each number in the Venn diagram. 4 1) 30 2) 5 3) √21 4) –√9 7 6 5) 0 6) –16 7) 8) √7 2 Determine whether each statement is true or false. If the statement is true, explain your reasoning. If the statement is false, provide a counterexample. 9) All whole numbers are rational numbers. 10) All real numbers are irrational numbers. NAME _____________________________________________ DATE ____________________________ PERIOD ____________ Practice: 1-1 The Real Number System Classify each number by determining all sets of numbers to which it belongs. 1) 0 2) –√36 3) 4 4) 6.3 5) 4.18 6) –11 Classify each number by determining all sets of numbers to which it belongs. Then write each number in the Venn diagram below. 7) 19 8) –6 9) 0 8 10) 11) 0.16 12) –√11 4 Determine whether each statement is true or false. If the statement is true, explain your reasoning. If the statement is false, provide a counterexample. 13) All whole numbers are natural numbers. 14) All irrational numbers are real numbers. 15) All rational numbers are integers. \ 16) An integer cannot be a rational number. NAME _____________________________________________ DATE ____________________________ PERIOD ____________ Notes: 1-1 The Real Number System Numbers may be classified by identifying to which of the following sets they belong. Natural Numbers Numbers used for counting. {1, 2, 3, 4, 5, …} Whole Numbers The set of natural numbers and 0. {0, 1, 2, 3, 4, …} Integers The set of whole numbers and their opposites {…, –2, –1, 0, 1, 2, …} a Rational Numbers Numbers that can be expressed in the form , where a and b are integers and b ≠ 0. b a Irrational Numbers Numbers that cannot be expressed in the form , where a and b are integers and b ≠ 0. b Classify each number by determining all sets of numbers to which it belongs. a. 5 b. 0.666… c. –√25 d. –√11 Classify each number by determining all sets of numbers to which it belongs. Then write each number in the Venn diagram. 4 1) 30 2) 5 3) √21 4) –√9 7 6 5) 0 6) –16 7) 8) √7 2 Determine whether each statement is true or false. If the statement is true, explain your reasoning. If the statement is false, provide a counterexample. 9) All whole numbers are rational numbers. 10) All real numbers are irrational numbers. .