Question

Which numbers can be shown on a number line?

Answer 1

Hint: For solving this problem, the knowledge of the number system and the diagrammatic representation of numbers on a number line is must. We can easily solve the problem once we know the exact value associated with different types of numbers in the number system.

Complete step-by-step answer:
The basic way of representing these numbers diagrammatically is by using a number line. 

A number line is a simple line having numbers marked on it to show various information associated with that point. In mathematics, the number system is the branch that deals with various types of numbers possible to form.
Types of numbers can be classified as:
Natural numbers, Whole numbers, Integers, Rational numbers, Irrational numbers, Real numbers and Imaginary numbers and Complex numbers.

We can see Natural numbers, Whole numbers, Integers, Rational numbers, Irrational numbers are a part of Real numbers. Fractions comes under Rational numbers.

Imaginary numbers are having $i=\sqrt{-1}$ which don't really exists but used in various fields of mathematics. Complex number is a combination of Real and imaginary numbers.

Except Imaginary numbers and complex numbers, Remaining all numbers can be represented uniquely on a number line.

Examples: Representing Integers on number line:

Representing Decimals on the number line:

Therefore, All Real numbers can be represented on a number line can be shown on the number line.

Note: 

Irrational numbers come under the category of Real numbers. Their exact value is not known but mathematicians have developed some method like the arc method to represent irrational numbers on a number line.