RD Sharma Class 10 Solutions Chapter 1 Exercise 1.6 (Updated for 2024)

RD Sharma Class 10 Solutions Chapter 1 Exercise 1.6: The questions in this exercise are designed to help students comprehend when a rational number’s decimal expansion is terminating and when it is non-terminating recurring. RD Sharma Solutions Class 10 is the best source for understanding the correct approaches for tackling such questions and achieving excellent exam scores. Students may also get the RD Sharma Solutions for Class 10 Maths Chapter 1 Real Numbers Exercise 1.6 PDF from the below link.

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RD Sharma Class 10 Solutions Chapter 1 Exercise 1.6 PDF

Access answers to RD Sharma Solutions Class 10 Maths Chapter 1 Exercise 1.6- Important Question with Answers

Question 1.

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

Solution:




Since, the denominator is of the form 2^m x 5ⁿ, the rational number has a terminating decimal expansion.

Question 2.
Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2^m x 5ⁿ, where m and n are non-negative integers:

Solution:

Question 3.
Write the denominator of the rational number \frac { 257 }{ 5000 } in the form 2^m x 5ⁿ , where m, n are non-negative integers. Hence, write the decimal expansion, without actual division.
Solution:

Question 4.
What can you say about the prime factorisations of the denominators of the following rationals :
Solution:
(i) 43.123456789
This decimal fraction is terminating Its denominator will be factorised in the form of 2^m x 5ⁿ where m and n are non-negative integers.

This decimal fraction is non-terminating repeating decimals.
The denominator of their fraction will be not in the form of 2^m x 5ⁿ where m and n are non-negative integers.

This decimal fraction is terminating
Its denominator will be factorised in the form of 2^m x 5ⁿ where m and n are non-negative integers
(iv) 0.120120012000120000 ………..
This decimal fraction in non-terminating non recurring
Its denominator will not be factorised in the form of 2^m x 5ⁿ where m and n are non negative integers

Question 5.
A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form \frac { p }{ q } ? Give reasons. [NCERT Exemplar]
Solution:
327.7081 is terminating decimal number. So, it represents a rational number and also its denominator must have the form 2^m x 5ⁿ.

Hence, the prime factors of q is 2 and 5.

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