NCERT Class 10 Solutions: Real Numbers (Chapter 1) Exercise 1.4 –Part 5

Download PDF of This Page (Size: 448K)

Q-3 The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form, what can you say about the prime factor of q?

Solution:

Types of Decimal Expansions

Types of Decimal Expansions

Types of Decimal Expansions

  1. Is terminating

    So, it would be a rational number

    Hence is now in the form of

    And the prime factors of q are in terms of 2 and 5

  2. Is non terminating and non-repeating

    So, it is not a rational number

    Therefore, the given number is an irrational number

  3. Here is non terminating but repeating decimal

    So, it would be a rational number of the form and q is not of the form

    That is the prime factors of q will also have a factor other than 2 or 5.

Understanding Terminating and Nonterminating Decimals

Understanding Terminating and Nonterminating Decimals

Understanding Terminating and Nonterminating Decimals

Sign In