Question

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 factors of q?
(1) 43.123456789
(i) 0.120120012000120000...
(iii) 43.123456789 ( bar from 1 to 9)​

Answer 1

(i) and (iii) are rational numbers while (ii) is an irrational number.

Explanation:

(i) 43.123456789 contains a certain number of digits that can be represented in the form of p/q.

∵ it is a rational number.  

Since it has a certain number of digits and the number which includes certain  number of digits is characterized always as a terminating number and for a terminating number, the  denominator only contains the prime factor of 2 and 5.

(ii) 0.120120012000120000. . .

The denominator's prime factor will not have a value =  2 or 5.

∵ It is an irrational number because it is non-repeating and non-terminating as well.

(iii) 43.  123456789 with bar

∵ It is a rational number as the bar symbolizes that the decimals repeat over and again.

So, it is non- terminating and a rational number.

Learn more: rational numbers

brainly.in/question/17198095

Answer 2

Explanation:

i hope it will help u........