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Home Class 10th Solutions 10th Maths

NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4

by Sudhir
December 4, 2021
in 10th Maths, Class 10th Solutions
Reading Time: 4 mins read
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In this post, we will share NCERT Class 10th Maths Book Solutions Chapter 1 Real Numbers Ex 1.4. These solutions are based on new NCERT Syllabus.

NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4

Question 1.
Without actually performing the long divison, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 1
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 2
Solution:
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 3
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 4
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 50
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 60

NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4

Question 2.
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.
Solution:
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 5
Multiplying and dividing by 25, we have
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 6
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 70

NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4

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
∴ The given decimal expansion terminates.
∴ It is rational of the form \(\frac{p}{q}\)
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 7
Hence, p = 43123456789 and q = 29 × 59
Prime factors of q are 29 and 59.

(ii) 0.120120012000120000…
∵ The given decimal expansion is neither terminating nor repeating.
∴ It is irrational number, hence cannot be written in p/q form.

(iii) \(43 . \overline{123456789}\)
∵ The given decimal expansion is non-terminating repeating.
∴ It is rational number.
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 8
Multiplying both sides by 1000000000, we have
1OOOOOOOOOx = 43123456789.123456789…
… (2)
Subtracting (1) from (2), we have
(1000000000x) – x
= (43123456789.123456789 ) – 43.123456789…
⇒ 999999999x = 43123456746
NCERT Class 10th Maths Solutions Chapter 1 Real Numbers Ex 1.4 9
Here, p = 4791495194 and q = 111111111, which is not of the form 2m × 5n i.e., the prime factors of q are not of the form 2m × 5n.

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