Question

Classify the number as rational or irrational.

Select Rational or Irrational for each number.

0.5
24−−√
3.42859873
0100

Answer 1

rational
irrational
rational
rational

Answer 2

0.5 = Rational number,

√24 = Irrational number,

3.42859873 = Rational number,

0100 = Rational number

Explanation:

Rational number is a real number that can be expressed as
`(p)/(q)`,

Where, both p and q are integers and q ≠ 0,

Otherwise the number is called irrational number.

(i) Since, 0.5 = 5/10,

Where, both 5 and 10 are integers,

And, q ≠ 0,

So, 0.5 is a rational number.

(ii) Since, √24 = √(6×4) = 2√6

But, √6 is irrational number and 2 is rational number,

We know that the product of irrational number and rational number is also irrational number,

⇒ √24 is an irrational number.

(iii)

`3.42859873 = (342859873)/(100000000)`

Where, both 342859873 and 100000000 are integers,

And, 100000000 ≠ 0,

So, 3.42859873 is a rational number.

(iv) 100 is an integer,

An integer is always a rational number,

⇒ 100 is a rational number.