Question

Name all sets of numbers to which each real number belongs.
1) 12
2) -15
3)1 1/2
4) 3.18
5) square root 48
6) 9.3
7) -2 7/9
8) square root 25
9) square root 3
10) negative square root 64
11) negative square root 12
12)8/4

Answer 1

Answer and Explanation:

To find : Name all sets of numbers to which each real number belongs ?

Solution :

Real number is defined as a set which contain all rational, irrational, integers, whole number, natural number.

Real number not contain an imaginary number i.e. i.

Now, Determining each number

1) 12 is real, rational, whole, integer.

2) -15 is real, rational, integer.

3) $1\frac{1}{2}=\frac{3}{2}=1.5$ is real, rational

4) 3.18 is real, rational

5) $\sqrt{48}=6.92820323028...$ is real and irrational because non-terminating and non-repeating.

6) 9.3 is real, rational

7) $-2\frac{7}{9}=-\frac{25}{9}=-2.7777777....$ is a real, rational as it is repeating decimal.

8) $\sqrt{25}=\pm 5$ is a real, rational, integer.

9) $\sqrt{3}=1.73205080757...$ is real and irrational because non-terminating and non-repeating.

10) $-\sqrt{64}=-8$ is real, rational , integer.

11) $-\sqrt{12}=-3.46410161$ is real, irrational because non-terminating and non-repeating.

12) $\frac{8}{4}=2$ is real, rational, whole, integer.

Answer 2

The set of real numbers in which the given numbers belong to are given based on the description and properties of the real number types explained below;

Real numbers are composed of the following set of numbers : Whole numbers, natural numbers, integers, rational numbers and irrational numbers.

• Natural numbers include all positive numbers which may be used for ordering or counting. They include numbers from 1,  till infinity.

• Whole numbers include all positive integer values including 0.

• Integer numbers are the set of all positive and negative whole number values including 0. Examples are : (-1, 0, 8)

• Irrational numbers are non-integer values which cannot be expressed in the form a/b. Such as (√5, 1.7171...)

Using the definitions above :

• 12 = Natural, whole number , integer and rational (12/1)

• -15 = Integer, rational (-15/1)

• 1 1/2 = 3/2 = Rational

• 3.18 = rational (terminating decimal)

• square root 48 = √48 = 6.928... = irrational(non-terminating and non-repeating)

• 9.3 = rational (terminating decimal)

• -2 7/9 = -25/9 = rational (a/b)

• square root 25 = √25 = ±5 = integer, rational (5/1)

• square root 3 = √3 = 1.732... irrational number (non-terminating and non-repeating) .

• negative square root 64 = - √64 = - 8 = integer, rational (-8/1)

• negative square root 12 = - √12 = - 3.464... = irrational (non - terminating)

• 8/4 = 2 = natural, whole number, rational, integer

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