A. -4 rational
B. 3/10 rational
C. 4.51010910921... irrational
D. .987987987987... rational (repeating pattern)
Answer: The correct options are
(A) -4
(B) [tex]\dfrac{3}{10}[/tex]
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
[tex]\dfrac{3}{10}=0.3.[/tex]
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.
