Question

which of the following is not a rational number? (a).2.635, (b).3.264426444, (c).7.00400040000. (d). 1.002002002​

Answer 1

Answer:

All the rational number

Answer 2

Solution :-

We know that,

• A number which can be written in the form of p/q where q ≠ 0 are called as rational numbers .
• Non - terminating, non - repeating decimals are irrational numbers .

So, checking given options now,

(a)2.635

→ 2635/1000

→ 527/200

since given decimal is written in the form of p/q and q is also not equal 0 . Therefore, given decimal is a rational number .

(b)3.26442644___

→ 3.2644 (bar on 2644)

Let,

→ x = 3.26442644____

multiply both sides by 10000

→ 10000x = 32644.2644______

subtracting both,

→ 10000x - x = 32641

→ 9999x = 32641

→ x = 32641/9999

since given decimal is written in the form of p/q and q is also not equal 0 . Therefore, given decimal is a rational number .

(c) 7.00400040000

as we can see that, here numbers after decimals are non - terminating, non - repeating . Therefore, it is an irrational number .

(d)1.002002002

→ 1.002 (bar on 002)

Let

→ x = 1.002002_____

multiply both sides by 1000,

→ 1000x = 1002.002_____

subtracting both,

→ 999x = 1001

→ x = 1001/999

since given decimal is written in the form of p/q and q is also not equal 0 . Therefore, given decimal is a rational number .

Hence, we can conclude that, Option (c) is not a rational number .

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