**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

*. Hence, this decimal expansion is terminating.*^{m}Since the denominator is of the form 2

*so, this decimal expansion is terminating.*^{m}Since the denominator can not be written in the form 2

^{m}^{ }× 5*and it also contains other factors 7 and 13, so its decimal expansion will be non-terminating repeating type.*^{n}As the denominator is of the form 2

^{m}^{ }×^{ }5*so, the above decimal expansion is terminating.*^{n}Since the denominator can not be written in the form 2

^{m}^{ }× 5*and it has 7 as its factor so, the decimal expansion of is non-terminating repeating.*^{n}The denominator is of the form 2

^{m}^{ }× 5*therefore, it is a terminating decimal expansion.*^{n}Since the denominator is not of the form 2

^{m}^{ }× 5*, and it also contain another factor 7 so, the above decimal expansion is non-terminating repeating.*^{n}The denominator can be written in the form 2

^{m}^{ }× 5*. Hence, the above decimal expansion is terminating.*^{n}Since the denominator is of the form 2

^{m}^{ }× 5*so, the above decimal expansion is a terminating one.*^{n}Since the denominator is not of the form 2

^{m}^{ }× 5*and also contains 3 as its factors so, the above decimal expansion is non-terminating repeating.*^{n}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 5^{n}i.e., the prime factors of*q*will also have a factor other than 2 or 5.
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