Question

(2) In the simplest form of rational numbers p&q (q+0) are integers having no common factor other than..​

Answer 1

Step-by-step explanation:

Look at the several examples of rational numbers in the form p/q (q ≠ 0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions).

Answer 2

Answer:

We shall look at some examples of rational numbers in the form of p/q (q ≠ 0), where their decimal representations are terminating.

2/5 = 0.4

3/100 = 0.03

27/16 = 1.6875

33/50 = 0.66

Let's observe the denominators of the above rational numbers.

2/5 = 2 / (20 × 51)

3/100 = 3 / (22 × 52)

27/16 = 27 / (24 × 50)

33/50 = 33 / (21 × 52)

We observe that the denominators of the above rational numbers are in the form of 2a × 5b, where a and b are whole numbers.

Hence if q is in the form 2a × 5b then p/q is a terminating decimal.