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What is Number Line?

Number lines

Understanding the concept of the number line can be considered the first step of learning mathematics. The first thing taught for learning high-order math is the number line. But what is a number line? 

Let us split the word number line into two individual words, number and line. Numbers, as we all know, are 0, 1, 2, 3, 4,…….., infinity. The line indicates a length extending from one point to another having no width. Thus we can say that a number line is a line that contains numbers on it. 

Definition of a Number Line 

A number line is the simplest graph that depicts numbers in a straight line. This line compares integers that are evenly spaced on an endless line that extends horizontally or vertically on both sides. 

Locating Numbers on a Number Line

On a number line, arithmetic operations of numbers can be better described. First, one needs to understand how to find numbers on a number line. A number line’s midway point is zero. Positive numbers inhabit the right side of the zero on the number line, whereas negative numbers fill the left side of the zero. The value of a number falls as we travel from 0 to the left side and increases as we move from 0 to the right side. 

Like the integers, fractions, and decimals, almost every number, rational, irrational numbers can be simply expressed on a number line. The only numbers that cannot be depicted on the number line are imaginary. They are represented on a special number line known as the Argon plot. In this article, we shall only focus on numbers represented on the number line.  

Negative and Positive Number Line

As described earlier, the positive and negative numbers are the two sorts of numbers represented on a number line. Let us learn more about this segment’s positive and negative number lines. 

A negative number line is the segment of the number line on the left side of zero. The area on the right side of zero, on the other hand, is known as a positive number line since it contains all positive integers. From both ends, it may be extended indefinitely. There is no boundation on how long a number line can be. It can be as short as to fit inside your notebook and as long as to cover the entire earth a million times. Below are some of the qualities of the negative and positive number lines. 

  • The numbers on the right are greater in value than those on the left.
  • The left-hand numerals are smaller in value than the right-hand numbers.
  • The point of origin, or the midpoint of the number line, is 0 (zero).
  • The numbers are spaced out evenly. This means that if you have to make a number line, you have to take numbers arranged in a proper sequence. A number line cannot be made like 1, 2, 5, 11,…….99. A number line is always made with proper spacing like 5, 10, 15, 20, ……., 100 or 1, 3, 5, 7, ….. 99, etc.

In the next section of this article, you will understand this concept in detail, where we shall learn how to make/draw a number line.

How to Draw a Number Line?

Read this step-by-step procedure created by our expert faculty, which will help you easily understand the concepts of number lines. 

  • Step 1: Make a straight horizontal or vertical line (choice is yours) on a sheet of paper. Add two arrows at both ends. These arrows specify that the line extends to infinity on the left and the right side. 
  • Step 2: This step is the most crucial. This step involves choosing an appropriate scale to make the markings on the number line. For instance, if you have to plot numbers from 0 to 4, then you can choose a scale of 1 or 2. For a scale of 1, the numbers on the number line shall be 0, 1, 2, 3, and 4. On a scale of 2, the numbers on the number line will be 0, 2, and 4. Thus choose your scaling accordingly with an equal number of intervals between any two numbers.  
  • Step 3: Again, consider the number line from 0 to 4. You have already fixed the interval as 1, so the points will be 0, 1, 2, 3, and 4. The third step involves marking all these points. They will act as identifiers. 
  • Step 4: The final step is to find the number of your choice and highlight it with the help of a circle. 

This is how you can easily draw and mark any number on the number line. We have learned concepts related to the number line with natural numbers, whole numbers, and integers. We shall know how to depict decimals and fractions on a number line in the next modules.

Number Line with Decimals

Decimal numbers contain a whole number part and a fractional part separated by the dot. For example, 13.3353, where 13 is the whole number part while 3353 is the fractional part of the decimal. But how do we represent this on the number line? Follow the steps mentioned below to completely grasp the concept of marking a decimal point on the number line. 

For instance, represent 1.8 on the number line?

  • Step 1: Draw a straight line. 
  • Step 2: Find the whole number and the fractional number. In this case, 1 is the whole number, and 0.8 is the fraction. According to the whole number mark numbers with equal intervals. In this case, 0, 1, and 2.
  • Step 3: We know that 1.8 lies between 1 and 2, making smaller marks with a value of 0.1 each. Make ten equal intervals from 1 to 2. Thus, the numbers between 1 and 2 are 1.1, 1.2, 1.3,….., and so on.
  • Step 4: Find 1.8 and mark it with a circle.

This is how you mark any decimal point on the number line. Hope you all must have understood the concept. 

Inequalities on a Number Line

We have learned how to mark numbers equal to integers or decimals until now. In this section, we shall learn how to deal with inequalities. Inequality means all the numbers are either greater or smaller than a specified number. Inequality is the concept of comparing two or more quantities together. The symbols used for depicting inequalities are less than symbol ‘<’, less than equal to symbol ‘<=’, greater than symbol ‘>’, greater than equal to symbol ‘>=’, and not equal to ‘≠’ symbol. 

To understand inequality on a number line, look at the example below and follow the steps mentioned in the example:

For instance, represent a <= 3 on the number line.

Solution: 

  • Draw a straight line and mark the starting point 0 anywhere on the line. 
  • It is given that a <= 3, therefore mark a point 3 on the right side of 0 by taking equal intervals of 1. Thus the points will be 0, 1, 2, 3.
  • Make a circle at three and start to shade to the left side of 3 (from 2 to 0).
  • This shaded region is the inequality required in the example.

Remember these points while solving problems related to inequality:

  1. ‘Greater than equal to x’ and ‘less than equal to x’ means that the number x must also be included in the shading.
  2.  ‘Greater than x’ and ‘less than x’ means that the number x must not be included while shading the inequality. 
  3. Negative numbers follow the rules opposite to that of positive numbers. In a negative number larger the number after a negative sign, the smaller is the value of that integer. For example, -10 is greater than -20. In reality, -1 is the greatest negative integer. 

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