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Understand Rational Numbers: Concept & Examples

Grade 7
Sep 15, 2022

Key Concepts

  • Write rational numbers in decimal form: terminating decimals  
  • Write rational numbers in decimal form: repeating decimals
  • Recognize rational numbers in decimal form

1.2 Understand Rational Numbers 

What is a rational number? 

A rational number is a number that is of the form , where p and q are integers and q ≠ 0. Rational numbers are denoted by Q . 

How to identify rational numbers? 

To identify if a number is rational or not, check the below conditions. 

  • It is represented in the form of p/q, where q≠0. 
  • The ratio p/q can be further simplified and represented in decimal form. 
  • All whole numbers are rational numbers

Decimal Representation of Rational Numbers: 

Rational numbers can be expressed in the form of decimal fractions. 

A rational number can have two types of decimal representations: 

  • Terminating 
  • Non-terminating 

Terminating decimals: 

Terminating decimals are those numbers which come to an end after few repetitions after decimal point. 

Example: 0.5, 2.456, 123.456, etc. are all examples of terminating decimals. 

Non terminating decimals (repeating): 

Non terminating decimals are those which keep on continuing after decimal point. They do not come to an end or if they do it is after a long interval. 

Example: 1/7= 0.1428571…. which is a non-terminating repeating decimal. 

Example 1: 


Convert the fraction, 5/8 to a decimal. 

So,5/8 = 0.625. This is a terminating decimal. 

Example 2: 

Convert the fraction 7/12 to a decimal. 

7/12= 0.583. This is a repeating decimal. 

The bar over the number, in this case 3, indicates the number or block of numbers that repeat unendingly. 

Example 3: 

The length and breadth of a rectangle are 7.1 inches and 2.5 inches respectively. Determine whether the area of the rectangle is a terminating decimal or not. 

Solution: Given, the length of rectangle is 7.1 inches and the breadth of rectangle = 2.5 inches. 

Area of Rectangle = Length × Breadth = 7.1 inches × 2.5 inches =17.75 inches. 

As the number of digits is finite after the decimal point, the area of rectangle is a terminating decimal expansion. 

Example 4: 

Write 5/3 in decimal form. 

Using long division method, we will observe the steps in calculating 5/3

Therefore, 1.666… is a non-terminating repeating decimal and can be expressed as 1.6.


Classify the following decimal fractions as terminating and non-terminating recurring decimals.

  1. 0.777…
  2. 0.777
  3. 4.7182
  4. 4.7182
  5. 9.1651651…….
  6. 9.165
  7. 0.52888…….
  8. 0.528
  9. 72.13
  10. 10.605

What have we learnt:

  • Understand the meaning of rational numbers
  • Identify positive and negative integers
  • Write the rational numbers in the form
  • Write rational numbers as decimal form
  • Differentiate between terminating and non-terminating decimals
  • Solve problems on rational numbers

Concept Map


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