10th Class NCERT (CBSE) Mathematics | Chapter 1, REAL NUMBERS | Math Textbook Exercise 1.4 (Solution)

Class 10, Ncert Cbse Mathematics 

Chapter 1 Real Numbers

NCERT Math Solutions (Exercise 1.4)

(Page 17)

Q1: 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:

The denominator can be written in the form 5^m. Hence, this decimal expansion is terminating.

Since the denominator is of the form 2^m so, this decimal expansion is terminating.

 

Since the denominator can not be written in the form 2^m × 5ⁿ and it also contains other factors 7 and 13, so its decimal expansion will be non-terminating repeating type.

 

As the denominator is of the form 2^m × 5ⁿ so, the above decimal expansion is terminating.

Since the denominator can not be written in the form 2^m × 5ⁿ and it has 7 as its factor so, the decimal expansion of is non-terminating repeating.

The denominator is of the form 2^m × 5ⁿ therefore, it is a terminating decimal expansion.

Since the denominator is not of the form 2^m × 5ⁿ, and it also contain another factor 7 so, the above decimal expansion is non-terminating repeating.

The denominator can be written in the form 2^m × 5ⁿ. Hence, the above decimal expansion is terminating.

Since the denominator is of the form 2^m × 5ⁿ so, the above decimal expansion is a terminating one.

Since the denominator is not of the form 2^m × 5ⁿ and also contains 3 as its factors so, the above decimal expansion is non-terminating repeating.

Q2: Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions.

Solution: 

Q3: 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 p/q, what can you say about the prime factor of q?

Solution:

(i) 43.123456789

This number has a terminating decimal expansion. So, it is a rational number of the form p/q and q is of the form

 (ii) 0.120120012000120000 …

The given decimal expansion is non-terminating and non-recurring. Therefore, it is an irrational number.

Since the given decimal expansion is non-terminating, so it is a rational number of the form p/q and q is not of the form 2^m x 5ⁿ i.e., the prime factors of q will also have a factor other than 2 or 5.