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Name _______________________________ Date ___________ Number and Operations Real Number Properties Which of the numbers on the top row of this number line are real numbers? Circle the real numbers on the top row and explain how you can tell. All points on a number line are real numbers. What is a whole number? Write a definition, then give 5 examples. Whole numbers include all counting numbers and 0. Some examples are 5, 37, 99, 450, and 90,734. What numbers are integers? Write 5 examples. The set of integers includes all whole numbers and their opposites and zero. Some examples are 3, –9, 461, –22, –833, and 0. What is a rational number? What kinds of decimal numbers are rational numbers? Rational numbers can be written as fractions. Terminal or repeating decimal numbers are rational numbers. Write examples of 5 different kinds of rational numbers. Correct answers include any positive or negative whole number, fraction, or terminal or 3 7 7 repeating decimal number, such as 231, –71, , 0, – 5 , , 0.75, and 9.33. 5 8 9 © 2003 CompassLearning, Inc. Page 1 Activity 76237 Name _______________________________ Date ___________ Number and Operations Real Number Properties Which of these numbers are irrational? Circle them and explain why they are irrational. 2 π 7 The square root of 5 and pi are irrational numbers, because they cannot be written as 49 0.3333 0.760 5 fractions, and they are not terminating or repeating decimal numbers. Explain what the bar means in this decimal number: 2.2360 . Show a longer way of writing the decimal number. The bar marks the digits that are repeating. It’s a shorter way of writing 2.23606060…. 8 to a decimal number and write the result. What kind of 55 decimal number is it, and what is the simplest way to write it? Explain how to convert The bar in a fraction means “divided by.” To convert a fraction to a decimal number, divide the numerator by the denominator: 8 ÷ 55 = 0.1454545. It’s a repeating decimal number, which can be written more simply as 0.145 . Which of these decimal numbers is greater? Explain how to determine this. 0.78 or 0.78 The decimal numbers can be compared by extending each of them. Write each as a repeating decimal number: 0.787878 and 0.788888. Comparing the thousandths place, you can see that 0.788 is greater than 0.787. So 0.78 > 0 .78 . © 2003 CompassLearning, Inc. Page 2 Activity 76237 Number and Operations Name _______________________________ Date ___________ Real Number Properties Write each of these numbers in every group in which it belongs. 362 – 23 Whole Numbers 6 1 7 Integers Rational 362 362 –23 1 6 0.6 7 – 81 – 362 – 23 81 – 8 0.6 Irrational 81 Real 362 –23 1 6 0.6 7 8 – 81 8 Write each of these numbers in every group in which it belongs. 6.1428571… Whole Numbers – – 14.2 7 9 Rational Integers – 0 0 822 822 π 0.4545 14.2 − 7 9 0 822 © 2003 CompassLearning, Inc. Page 3 0.01 Irrational 0.4545 .01 0 6.1428571… 7 π 7 822 Real 6.1428571… 7 – 14.2 – 9 0.4545 π 0 0.01 7 822 Activity 76237