## 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 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 ? 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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