Look at several examples of rational numbers in the form \( \frac{p}{q}\) (q \( \ne\) 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

Asked by Vishal kumar | 2 years ago | 272

Let us we take the examples \( \frac{5}{2}, \frac{5}{4}, \frac{2}{5}, \frac{2}{10}, \frac{5}{16}\) of the form \( \frac{p}{q}\) that are terminating decimals.

\( \frac{5}{2}\) = 2.5

\( \frac{5}{4}\) = 1.25

\( \frac{2}{5}=0.4\)

\( \frac{2}{10}=0.2\)

\( \frac{5}{16}=0.3125\)

We can observe that the denominators of the above rational numbers have powers of 2, 5 or both. Therefore, q must satisfy in the form either \( 2^m\) or \( 5^n\) or both \( 2^m\times 5^n\) (where m = 0, 1, 2, 3....... and n = 0, 1, 2, 3......) in \( \frac{p}{q}\) form.

Answered by Shivani Kumari | 2 years agoVisualise the representation of \( 5.3\overline{7}\) on the number line upto 5 decimal places, that is upto 5.37777.

Visualise 2.665 on the number line, using successive magnification.

Find whether the following statements are true or false:

**(i) **Every real number is either rational or irrational.

**(ii)** π is an irrational number.

**(iii)** Irrational numbers cannot be represented by points on the number line.