## RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.6

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.6

Other Exercises

- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.1
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.2
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.3
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.4
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.5
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.6
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers VSAQS
- RD Sharma Class 10 Solutions Chapter 1 Real Numbers MCQS

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 5^{n}, 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 5^{n}, 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 5^{n} , 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 5^{n} 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 5^{n} 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 5^{n} 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 5^{n} 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 5^{n}.

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

Hope given RD Sharma Class 10 Solutions Chapter 1 Real Numbers Ex 1.6 are helpful to complete your math homework.

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