CLASSIFYING RATIONAL AND IRRATIONAL NUMBERS

A rational number is a type of real number, which is in the form of p/q where q is not equal to zero.

Any fraction with non-zero denominators is a rational number.

Integers are rational numbers ?

Yes

For example,

-5, -4, -3, ....., 0, 1, 2, 3,..........

Every numbers can be written as a fraction, so they are rational.

Whole numbers are rational numbers ?

Yes

Is 0 a rational number ?

Yes

0 can be considered as fraction with any denominator.

Classify each number as RATIONAL (Q) or IRRATIONAL (I)

Problem 1 :

√47

Solution :

√47 is an irrational, because 47 is not a perfect square.

√47 = 6.8556546….. (irrational)

6.8556546….. is a non terminating and non repeating decimal.

So, √47 is irrational number.

Problem 2 :

11/9

Solution :

11/9

11/9 is in the form of a/b

11/9 is a rational number.

Problem 3 :

19/4

Solution :

19/4

19/4 is in the form of a/b

19/4 is a rational number.

Problem 4 :

√96

Solution :

√96 is an irrational, because 96 is not a perfect square.

√96 = 9.7979589711….. (irrational)

√96 is irrational.

Problem 5 :

19/14

Solution :

19/14

19/14 is in the form of a/b

19/14 is a rational number.

Problem 6 :

15/4

Solution :

15/4

15/4 is in the form of a/b

15/4 is a rational number.

Problem 7 :

√84

Solution :

√84 is an irrational, because 96 is not a perfect square.

√84 = 9. 161513….. (irrational)

√84 is irrational number.

Problem 8 :

-9

Solution :

-9

-9/1 is in the form of a/b

-9 is a rational number.

Problem 9 :

√72

Solution :

√72 is an irrational, because 96 is not a perfect square.

√72 = 8.48528137….. (irrational)

√72  is irrational number.

Problem 10 :

0

Solution :

0

0/1 is in the form of a/b

0 is a rational number.

Problem 11 :

8/9

Solution :

8/9

8/9 is in the form of a/b

8/9 is a rational number.

Problem 12 :

3

Solution :

3

3/1 is in the form of a/b

3 is a rational number.