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

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, Equation what can you say about the prime factor of q?

  1. Equation

  2. Equation

  3. Equation

Solution:

Types of Decimal Expansions

Types of Decimal Expansions

Types of Decimal Expansions

  1. Equation

    Equation Is terminating

    So, it would be a rational number

    Equation

    Equation

    Equation

    Equation

    Hence Equation is now in the form of Equation

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

  2. Equation

    Equation Is non terminating and non-repeating

    So, it is not a rational number

    Therefore, the given number is an irrational number

  3. Equation

    Here Equation is non terminating but repeating decimal

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

    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

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