Question

List the (a) Whole numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers for the given set of numbers :

Short answer

(a) Whole numbers :$0$.

(b) Integers : $-6,0$.

(c) Rational numbers :$-6,-\frac{5}{2},0,0.\overline{714285},2\frac{1}{5},\sqrt{14}$.

(d) Irrational numbers : No irrational number present in the given set of numbers.

(e) Real numbers :$-6,-\frac{5}{2},0,0.\overline{714285},2\frac{1}{5},\sqrt{14}$.

Step-by-step solution

Given Information.

The given set of numbers is : $-6,-\frac{5}{2},0,0.\overline{714285},2\frac{1}{5},\sqrt{14}$.

We need to classify them into the categories of (a) Whole numbers, (b) Integers, (c) Rational numbers, (d) Irrational numbers, (e) Real numbers.

Defining the categories .

(a) Whole numbers : zero and all natural numbers which are not fraction or decimal

(b) Integers : The whole numbers that can be positive, negative or zero.

(c) Rational numbers : Numbers that are written as the ratio of two integers, in which the denominator should not be zero.

(d) Irrational numbers : Any number that cannot be written as a fraction of a whole number.

(e) Real numbers : Rational numbers and irrational numbers and all the other numbers except complex numbers is a real number.

Listing the given set of numbers into their categories.

(a) Whole numbers :$0$.

(b) Integers :$-6,0$.

(c) Rational numbers : $-6,-\frac{5}{2},0,0.\overline{714285},2\frac{1}{5},\sqrt{14}$.

(d) Irrational numbers : No irrational number present in the given set of numbers.

(e) Real numbers :$-6,-\frac{5}{2},0,0.\overline{714285},2\frac{1}{5},\sqrt{14}$.