Question

Given each set of numbers, list the a) natural Numbers b) whole numbers c) integers d) rational numbers e) irrational numbers f) real numbers {-6, sqrt23, 21, 5.62, 0.4, 3 2/9, 0, -7/8, 2.074816...}

Irrational numbers
Given each set of numbers, list the
a) natural Numbers
b) whole numbers
c) integers
d) rational numbers
e) irrational numbers
f) real numbers
$$\displaystyle{\left\lbrace-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots\right\rbrace}$$

2021-02-02
a) Natural numbers:
The numbers that are used for counting are called natural numbers i.e. 1,2,3,…
And is represented by N. From the given set of numbers, natural numbers are: 21
b) Whole numbers:
Natural numbers along with 0 together are called the whole numbers i.e. 0,1,2,3…
And is represented by W. From the given set of numbers, whole numbers are: 21,0
c) Whole numbers along with negative numbers are called the integers i.e. …-3,-2,-1,0,1,2,3…
And is represented by Z. From the given set of numbers, integers are: -6, 21, 0
d) Rational Numbers:
The numbers that can be expressed in the form of $$\displaystyle\frac{{p}}{{q}}$$ are called the rational numbers and are represented by Q. This includes natural numbers, whole numbers and integers.
From the given set of numbers, rational numbers are: $$\displaystyle-{5},{21},{5.62},{0.4},{3}\frac{{2}}{{3}},{0},-\frac{{7}}{{8}}$$
e) Irrational Numbers:
The numbers that cannot be expressed in the form of $$\displaystyle\frac{{p}}{{q}}$$ are called the irrational numbers and are represented by Q'.
From the given set of numbers, irrational numbers are: $$\displaystyle\sqrt{{23}},{2.074816}\ldots$$
d) Real Numbers:
The set of rational and irrational numbers together are called real numbers.
And is represented by R.
From the given set of numbers, real numbers are: $$\displaystyle-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots$$