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

  1. 43.123456789

  2. 0.120120012000120000

  3. 43.123456789¯

Solution:

Types of Decimal Expansions

Types of Decimal Expansions

Types of Decimal Expansions

  1. 43.123456789

    43.123456789 Is terminating

    So, it would be a rational number

    43.123456789=431234567891000000000

    =43123456789(10)9

    =43123456789(2×5)9

    =4312345678929×59

    Hence 43.123456789 is now in the form of pq

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

  2. 0.120120012000120000

    0.120120012000120000 Is non terminating and non-repeating

    So, it is not a rational number

    Therefore, the given number is an irrational number

  3. 43.123456789¯

    Here 43.123456789¯ is non terminating but repeating decimal

    So, it would be a rational number of the form pq and q is not of the form 2n×5m

    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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