Question

BRAINLIESSSTTT!!!

Answer 1

A. -4    rational

B. 3/10   rational

C. 4.51010910921...   irrational

D. .987987987987...   rational  (repeating pattern)

Answer 2

Answer: The correct options are

(A) -4

(B) $\dfrac{3}{10}$

and

(D) 0.987987987987...

Step-by-step explanation:  We are given to select the numbers that are rational from the given options.

We know that

a decimal number is said to be a

(i) rational, if the digits after the decimal are either repeating or terminating

and

(ii) irrational, if the digits after the decimal are non-repeating and non-terminating.

Option (A) :  Here, the number is -4. This can be written as 4.00.

Since the digits after the decimal are terminating, so -4 is a rational number.

So, this option is correct.

Option (B) :  Here, the number is

$\dfrac{3}{10}=0.3.$

Since the digits after the decimal are terminating, so it is a rational number.

So, this option is correct.

Option (C) :  Here, the number is 4.51010910921....

Since the digits after the decimal are non-terminating and non-repeating, so it is an irrational number.

So, this option is NOT correct.

Option (D) :  Here, the number is  .987987987987...

Since the digits after the decimal are repeating, so it is a rational number.

So, this option is correct.

Option (E) : Since the number in option (C) is not rational, so there is a number listed that is not rational.

So, this option is NOT correct.

Thus, (A), (B) and (D) are correct options.