All numbers that will be pointed out in this class belong come the collection of the actual numbers. The set of the genuine numbers is denoted through the price \mathbbR.There are five subsetswithin the set of actual numbers. Let’s go over each among them.

You are watching: Name the sets of numbers to which each number belongs

Five (5) Subsets of actual Numbers

1) The collection of natural or counting Numbers

The set of the herbal numbers (also well-known as count numbers) includes the elements,


The ellipsis “…” signifies that the numbers go on forever in the pattern.

2) The collection of totality Numbers

The set of whole numbers consists of all the aspects of the organic numbers to add the number zero (0).


The slight enhancement of the element zero to the collection of organic numbers generates the new set of whole numbers. Basic as that!

3) The collection of Integers

The collection of integers consists of all the facets of the collection of totality numbers and the opposites or “negatives” of all the aspects of the collection of counting numbers.


4) The collection of rational Numbers

The set of rational numbers has all number that can be created as a portion or as a proportion of integers. However, the denominator cannot be equal to zero.


A reasonable number may likewise appear in the form of a decimal. If a decimal number is repeating or terminating, it deserve to be created as a fraction, therefore, it need to be a rational number.

Examples of terminating decimals:


5) The collection of Irrational Numbers

The collection of irrational numbers have the right to be described in many ways. These room the common ones.

a) Irrational numbers room numbers that cannot be written as a proportion of 2 integers. This description is specifically the opposite that of the rational numbers.

b) Irrational numbers are the leftover number after all rational numbers are eliminated from the set of the real numbers. You may think of it as,

irrational numbers = real numbers “minus” reasonable numbers

c) Irrational number if composed in decimal forms don’t terminate and don’t repeat.

There’s really no standard symbol to stand for the set of irrational numbers. But you might encounter the one below.


a) Pi

b) Euler’s number

c) The square root of 2

Here’s a rapid diagram the can help you classify genuine numbers.

Practice problems on exactly how to Classify actual Numbers

Example 1: tell if the declare is true or false. Every totality number is a organic number.

Solution: The set of whole numbers incorporate all natural or counting numbers and the number zero (0). Because zero is a entirety number the is no a organic number, as such the explain is FALSE.

Example 2: call if the declare is true or false. Every integers are entirety numbers.

Solution: The number -1 is an integer the is not a entirety number. This renders the explain FALSE.

Example 3: call if the explain is true or false. The number zero (0) is a rational number.

Solution: The number zero can be created as a ratio of 2 integers, for this reason it is indeed a rational number. This statement is TRUE.

Example 4: name the set or to adjust of numbers to i m sorry each real number belongs.

1) 7

It belongs to the set of organic numbers, 1, 2, 3, 4, 5, …. It is a entirety number because the collection of entirety numbers consists of the natural numbers to add zero. It is an integer since it is both a natural and whole number. Finally, since 7 can be created as a fraction with a denominator the 1, 7/1, then it is likewise a rational number.

2) 0

This is not a organic number because it cannot be discovered in the set 1, 2, 3, 4, 5, …. This is absolutely a whole number, an integer, and a rational number. That is rational since 0 can be expressed together fractions such as 0/3, 0/16, and 0/45.

3) 0.3\overline 18

This number obviously doesn’t belong to the collection of natural numbers, collection of entirety numbers and collection of integers. Observe that 18 is repeating, and so this is a reasonable number. In fact, we can write the a proportion of two integers.

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4) \sqrt 5

This is no a rational number because it is not feasible to compose it together a fraction. If us evaluate it, the square root of 5 will have a decimal worth that is non-terminating and non-repeating. This makes it an irrational number.

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