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4 years ago

BRAINLIESSSTTT!!!

Mathematics

2 answers:

DIA [1.3K]4 years ago

8 0

A. -4 rational

B. 3/10 rational

C. 4.51010910921... irrational

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

natali 33 [55]4 years ago

8 0

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.

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