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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