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The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. - CBSE Class 10 - Mathematics

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Question

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 p /q what can you say about the prime factors of q?

(1) 43.123456789

(2) 0.120120012000120000. . .

(3) `43.bar(123456789)`

Solution

(1) 43.123456789

It is a rational number and q will have factors of 2 and 5 only.

(2) 0.120120012000120000. . .

It is an irrational number as it is non-terminating and non-repeating.

(3) `43.bar(123456789)`

It is rational number, as it is non-terminating but repeating. The factors of q will be, apart from 2 and 5, some other factor also.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 1: Real Numbers
Ex. 1.40 | Q: 3 | Page no. 18

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Solution The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. Concept: Revisiting Rational Numbers and Their Decimal Expansions.
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