Question

Every point on the number line corresponds to a …….. number which may be either … or……..

Answer 1

Hint: First we will draw a number line and observe which kind of numbers a number line represents. A number line consists of points, each point represents a number. We will observe and then complete the given sentence.

Complete step by step solution:
A number line can be generally defined as a horizontal straight line in which numbers are placed at equal intervals. A number line can be extended infinitely in both the directions.

A number line contains all real numbers. Each point on the number line represents a different number. There are infinite points on the number line so each number represents either a rational or irrational number.
Real numbers include both rational and irrational numbers. A number line is also known as the real line.
So the complete sentence will be:
Every point on the number line corresponds to a unique real number which may be either rational or irrational.
The irrational number set and the rational number set together makes up the real number set. Hence, the number line is often referred to as the real number line.

Note: There arises confusion between natural numbers and real numbers. Natural numbers are also called counting numbers. They include only positive integers. Real numbers are the union of the rational numbers and irrational numbers. But as the number line has infinite points so there are infinitely many real numbers between any two given natural numbers.