Download File

Learning Station Activity 1: Real Numbers
Appendix_2b
Classification of Real Numbers
The diagram of "stack of funnels" below will help us classify any given real numbers easily. But
first, we need to describe what kinds of elements are included in each group of numbers. Each
group or set of numbers is represented by a funnel.
Funnels Relating the Sets of
Real Numbers
Learning Station Activity 1: Real Numbers
Appendix_2b
Real Number System
The natural numbers (also known as counting numbers) are the numbers that
we use to count. It starts with 1, followed by 2, then 3, and so on.
The whole numbers: Simply add the element zero to the current set of natural
numbers. Think of whole numbers as natural numbers together with zero.
The integers include all whole numbers and their opposites.
The rational numbers are numbers which can be expressed as ratio of integers.
That means, if we can write a given number as a fraction where the numerator
and denominator are both integers; then it is a rational number.
Rational numbers can also appear as a decimal. The decimal may terminate or
repeat.
Remember the denominator of a fraction cannot be zero. Any fraction with a
denominator of zero is undefined.
The irrational numbers are non terminating, non repeating decimals. π is an
irrational number.
The real numbers includes both the rational and irrational numbers.
Remember that under the rational number, we have the subcategories of
integers, whole numbers and natural numbers.
Learning Station Activity 1: Real Numbers
Appendix_2b
Directions: Identify the sets to which each of the following numbers belongs by marking an "X"
in the appropriate boxes.
Number
1.
−√17
2.
-12
3.
25
4.
0
5.
3.5
6.
5.46̅
7.
0. ̅̅̅̅̅
462
8.
22
9.
-15
10.
55
0
11. 2.010010001...
12.
13.
3
√22
√169
14.
√
25
64
15.
.235
16.
π
Natural
Whole
Integers
Numbers Numbers
Rational
Numbers
Irrational
Numbers
Real
Numbers
Learning Station Activity 1: Real Numbers
Appendix_2b
Directions: Read each statement below. Write true if the statement is true. Write false if the
statement is false. You may discuss your answer with your partner or group.
_____1.
Every integer is a rational number.
_____2.
Every rational number is an irrational number.
_____3.
Every natural number is an integer.
_____4.
Every integer is a natural number.
_____5.
Every real number is a rational number.
_____6.
Every natural number is a whole number
_____7.
Every integer is a natural number.
_____8.
Every rational number is a real number.
_____9.
Fractions can be part of the whole number system
_____10.
Negative numbers can be part of the real number system.
Answer each question below. Confer with your partner or group.
11.
Write one rational number between 4 and 5.
12.
Justify 3.020020002... is an irrational number.
13.
Does -1 + √2 lie on the negative side on the number line? Defend your reasoning.
14.
Insert two irrational numbers between 5 and 8 .
15.
How many rational numbers can be inserted between 2 and 7? Justify your answer.
3
7