Question

Is $-10$ rational , irrational, natural, whole, integer or real number?

Answer 1

In this question , we need to find whether $-10$ is rational , irrational, natural, whole, integer or real number. First we need to be clear with the definition of different sets of numbers and based on the theories of different sets of numbers we can find on which set does the given number belong. Then, we need to observe the given number $-10$ and need to find in which set this number belongs. We can proceed like this to get our answer.

Complete step by step solution:
Given, $-10$
Here we need to find $-10$ is rational , irrational, natural, whole, integer or real number.
There are many sets of numbers, namely rational numbers, irrational numbers, natural numbers, whole numbers, integers and real numbers.
To find whether the given number $-10$ belongs to the set of rational numbers, irrational numbers, natural numbers, whole numbers, integers or real numbers. We need to check if it satisfies the definition of each of these types of numbers.
1.Rational number is nothing but a number that can be written as a fraction which can be represented in the form of $\dfrac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$ .
2. Irrational number is nothing but a number that cannot be written in the form of a fraction with an integer in the numerator and an integer in the denominator and also irrational numbers do not include zero.
3. Natural numbers are known as the counting numbers which can take up values from $1$ to but excluding fractions .
4. Whole numbers are also known as the counting numbers which can take up values from $0$ to but excluding fractions.
5. Integer is nothing but a set of the whole numbers and their opposites.
6. Real number is nothing but a set of numbers which consists of every number from $- \infty$ to $\infty$ including zero and fraction, that is, real numbers are the union of both the rational and irrational numbers. They can be both positive or negative values.
Now on observing the given number $-10$ ,
We can rewrite $-10$ as $\dfrac{-10}{1}$ therefore $-10$ is the rational number since it is similar to the definition of the rational number.
The given number can’t be an irrational number because it is opposite to the definition of the irrational number. So $-10$ is not an irrational number.
Also $-10$ is not a counting number. So it is not a natural number and also not a whole number.
The number $-10$ is an integer since $10$ is the whole number and also integers are the set of the whole numbers and their opposites. Therefore $-10$ is an integer.
Also, the number $-10$ is a real number since it seems similar to the definition of the real number .
Thus we can tell that $-10$ is rational, integer and real numbers.
The given number $-10$ is rational, integer and real numbers.

Note:
The question here is regarding the given number $-10$ and where it belongs in the number system. We should be aware of the various types of numbers categorised in mathematics and how they differ from one another. We need to know that natural numbers are a subset of integers whereas integers are a subset of Rational Numbers and rational Numbers are a subset of the Real Numbers. Moreover, there are bigger sets than real numbers, that is the set of complex numbers which include all real and imaginary numbers. That is, the combinations of Real and Imaginary numbers make up the Complex Numbers.