**Real Numbers**

**Question 1.Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or non-terminating repeating decimal expansion:**

**Solution:**

**Question 2.Write down the decimal expansions of those rational numbers in the question 1, which have terminating decimal expansions.**

**Solution:**

**Question 3.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 , what can you say about the prime factors of q ?**

**(i)** 43. 123456789**(ii)** 0.120120012000120000…**(iii) **43.

**Solution:(i) **43.123456789

Here, the denominator is of the form 2

^{m}5

^{n}.

Hence, the number is a rational number, specifically a terminating decimal.

**(ii) **Since the given decimal number is non terminating non-repeating, it is not rational

**(iii)** Since the given decimal number is non terminating repeating, it is rational, but the denominator is not of the form 2^{m}5^{n}.