Rational Numbers on Number Line

Rational numbers are numbers that can be expressed as the fraction p/q, where p and
q are integers and q is not equals to 0. This set includes terminating decimals, repeating decimals, integers, and fractions. Examples include 3, -5, 2/4, and 0.75. Rational numbers can be plotted on a number line and are useful in real-life applications such as measuring distances, handling finances, and analyzing data. 

To represent rational numbers on a number line, we must follow the steps mentioned below:

Step 1: Draw a number line by marking 0 as the reference.

Step 2: Identify the integers between which the rational number lies and mark them. There will be two markings. For e.g., if the rational number is 3/4, then we have to mark 0 and 1 (two markings) as 3/4 lies between 0 and 1. 

Step 3: Divide the space between the two 0 and 1 into four equal parts as the rational number’s denominator. According to the example given above, we need to divide the space between 0 and 1 into four equal parts because in our example 3/4, the denominator is 4.  

Step 4: Starting from 0, move towards the right by counting the number of parts; the count should match the numerator of the rational number (in this case, 3). Once the count matches the value of the numerator, stop and mark the rational number that we need to represent.

Now, representing negative rational numbers on the number line is similar to the representation of positive rational numbers. However, only the direction of the movement is towards the left. All the steps described above remain the same. The only difference is they’re performed on the left side of the number line. 
 

The rational numbers on a number line have numerous applications across various fields. Let us see how they are used in different areas:

• Financial Transactions and Banking: For financial transactions, rational numbers are used mostly for accuracy. Positive numbers represent savings, while negative numbers indicate overdrafts or debts. 

• Temperature Measurement: Temperature scales, such as Celsius and Fahrenheit, use rational numbers to show temperature variations. A number line helps visualize temperature changes, especially when dealing with negative values, such as in winter forecasts. This helps meteorologists and individuals interpret weather conditions more effectively.

• Elevation and Sea Level Comparisons: Geographical elevations use rational numbers, where sea level is represented as 0. Positive values represent locations above sea level (like mountains), while negative values indicate depths below sea level (such as ocean trenches).