Question

Is $0$ a rational, irrational, natural, whole, integer or real number?

Answer 1

Verify the given statement:

First, recall the definition of rational numbers, irrational numbers, natural numbers, whole numbers, integers and real numbers.

$\bullet$Natural numbers: All the counting numbers that starts from $1$ and goes up to infinity, i.e., $1,2,3,...$. So, $0$ is not a natural number.

$\bullet$Whole numbers: All the counting numbers that starts from $0$ and goes up to infinity, i.e., $0,1,2,3,...$. So, $0$ is a whole number.

$\bullet$Integers: Integers include all the counting numbers and negative numbers but does not include fractions i.e., $...,-3,-2,-1,0,1,2,3,...$. So, $0$ is a integer.

$\bullet$Rational numbers: A number that can be written in the form $\frac{\mathrm{a}}{\mathrm{b}}$, where $\mathrm{a},\mathrm{b}$ are integers and $\mathrm{b}\ne 0$. So, $0$ is a rational number as it can be written as $\frac{0}{1}$.

$\bullet$Irrational numbers: A number that can not be written in the form $\frac{\mathrm{a}}{\mathrm{b}}$, where $\mathrm{a},\mathrm{b}$ are integers and $\mathrm{b}\ne 0$ . So, $0$ is not a irrational number.

$\bullet$Real numbers: A group of all the numbers that include rational and irrational numbers. Real numbers can be positive, negative or zero. So, $0$ is a real number.

Hence, $0$ is a rational number, whole number, integer and a real number.