CLASS 10 MATH NCERT SOLUTIONS FOR CHAPTER – 1 REAL NUMBERS EX – 1.4

Real Numbers

Question 1.
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or non-terminating repeating decimal expansion:

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers e4 1

Solution:

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers e4 2

NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers e4 3

Question 2.
Write down the decimal expansions of those rational numbers in the question 1, which have terminating decimal expansions.

Solution:
NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers e4 4

Question 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 \frac { p }{ q }, what can you say about the prime factors of q ?

(i) 43. 123456789
(ii) 0.120120012000120000…
(iii) 43. \overline { 123456789 }

Solution:
(i) 
43.123456789
NCERT Solutions for Class 10 Maths Chapter 1 Real Numbers e4 5
Here, the denominator is of the form 2m5n.
Hence, the number is a rational number, specifically a terminating decimal.

(ii) Since the given decimal number is non ­terminating non-repeating, it is not rational

(iii) Since the given decimal number is non terminating repeating, it is rational, but the denominator is not of the form 2m5n.

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