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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} × 5^{n} 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} × 5^{n} so, the above decimal expansion is terminating.

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

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

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

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

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

Solution:

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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