Question

Is $0.8$ real number, rational number, whole number, integer, irrational number?

Answer 1

Hint: Here we have to determine that $0.8$ is a real number, rational number, whole number, integer, irrational number. Firstly, we should know what are real numbers, rational numbers, whole numbers, integers and irrational numbers in order to determine whether $0.8$ is a real number, rational number, whole number, integer or irrational number. Real numbers include all rational numbers, whole numbers, integers and irrational numbers.

Complete step by step answer:
Real numbers: Real numbers can be defined as the numbers which can be represented on the number line or the number which we can think of is the real number. It includes all whole numbers, integers, rational numbers, irrational numbers. All the arithmetic operations can only be performed on these numbers. For example- $0,\,\,1,\,\,\sqrt 2 ,\,\,\dfrac{3}{2}$ etc.

Rational numbers: Rational numbers can be defined as the numbers which can be written in the form of a fraction where numerator and denominator are integers or the numbers which can be written in the form of $\dfrac{p}{q}$ where $q \ne 0$. These numbers also called terminating numbers means the number will end after some time digits by the decimal. For example- $\dfrac{1}{2},\,\,\dfrac{3}{5},\,\,\dfrac{4}{3}$etc.

Irrational numbers: The numbers which cannot be written in the form of $\dfrac{p}{q}$ because we cannot convert them in fraction form. So, these numbers are non-terminating means the number will never end after some digits. For example- $1.72346875 \ldots \ldots ,\sqrt 3 ,\sqrt 7 $ etc.

Whole numbers: The whole numbers can be defined as the number without fractions and they are a collection of all positive integers and zero. For example- $0,\,1,\,\,2,\,\,3 \ldots $etc.

Integers: An integer can be defined as any number that can be either $0$, positive number or negative number. An integer can never be a fraction, a decimal or a percent. All integers to the left of $0$ are negative integers and to the right are positive integers. For example- $ - 3,\, - 2,\, - 1,\,0,\,1,\,2$ etc.

Here, we have a number $0.8$. By the definition $0.8$ cannot be a whole number, integer and irrational number as whole numbers and integers can never be a decimal and also $0.8$ is a terminated number. We can write $0.8$ in a fraction as $\dfrac{8}{{10}}$. And we can also write $\dfrac{8}{{10}}$ as $\dfrac{4}{5}$. Therefore, $0.8$ is a rational number as we can represent it in the form of $\dfrac{p}{q}$ and also $q \ne 0$. As all rational numbers are real numbers so $0.8$ is a real number.

Hence, $0.8$ is a real number and a rational number but not a whole number, integer and irrational number.

Note: The top most category of the number is the complex number which is divided into real numbers and imaginary numbers. Real numbers are divided into rational numbers, whole numbers, integers, rational numbers and irrational numbers. Imaginary numbers do not exist in reality and cannot be used in real life calculations, they are expressed in terms of iota whose value is $\sqrt { - 1} $ and represented by $i$. Any complex number is represented in the form of $a + ib$ where $a$ and $b$ are real numbers.