#### Solved Examples and Worksheet for Classifying Rational and Irrational Numbers

Q1Is 814a rational number or an irrational number?

A. Rational
B. Cannot be determined
C. Irrational
D. None of the above

Step: 1
Any number which can be represented in the form of ab or cab, where a, b and c are integers and b ≠ 0, is a rational number.
Step: 2
A non-terminating and repeating decimal is also a rational number.
Step: 3
814
[Original number.]
Step: 4
= 334
[Convert from a mixed number to an improper fraction.]
Step: 5
= 8.25000
[Simplify.]
Step: 6
So, 814 is a rational number.
Q2Identify whether 400324 is a rational or an irrational number.
A. Rational number
B. Irrational number

Step: 1
400324 = 20 × 2018 × 18
Step: 2
= 2018 = 109, is a rational number.
Correct Answer is :   Rational number
Q3Identify whether 63 is a rational or an irrational number.

A. irrational number
B. rational number
C. none of the above

Step: 1
63 = (9 × 7) = 9 × 7 = 37
Step: 2
3 is a rational number, but 7 is an irrational number.
Step: 3
So, the product 37 is an irrational number.
Correct Answer is :   irrational number
Q4Identify the irrational number.
A. 2
B. 35
C. 25
D. 210

Step: 1
Irrational numbers are real numbers that cannot be expressed as fractions, terminating decimals, or repeating decimals
Step: 2
The value of 35 = 0.6.
Step: 3
The value of 2 = 1.41421356 .......
Step: 4
The value of 210 = 0.2
Step: 5
The value of 25 = 5
Step: 6
Among the choices given , only 2 is an irrational number.
Q5Identify the irrational number.
A. 32
B. 38
C. 56
D. None of the above

Step: 1
Irrational numbers are real numbers that cannot be expressed as fractions, terminating decimals, or repeating.
Step: 2
Among the choices, 56 = 9.1666...
Step: 3
32 = 1.5
Step: 4
38 = 0.375
Step: 5
So, none of the above is the answer.
Correct Answer is :   None of the above
Q6Identify the irrational number.
A. 125
B. 196
C. 65
D. 38

Step: 1
Irrational numbers are real numbers that cannot be expressed as fractions, terminating decimals, or repeating decimals
Step: 2
The value of 196 = 14
Step: 3
The value of 38 = 0.375
Step: 4
The value of 125 = 2.4
Step: 5
The value of 65 = 8.062...
Step: 6
Among the choices given, only 65 is an irrational number
Q7Which of the following is a rational number and a natural number?
A. - 25
B. 753
C. 139
D. 437.54

Step: 1
A rational number is the ratio of two integers in the form ab, where b ≠ 0.
Step: 2
Natural numbers are {1, 2, 3, ...}.
Step: 3
437.54 is a decimal number and a rational number.
Step: 4
- 25 is a negative rational number.
Step: 5
139 = 1.4444....is a repeating decimal number and a rational number.
Step: 6
753 = 25 is a natural number and a rational number.
Step: 7
Amongst the choices, 753 is the rational number and a natural number.
Q8Identify an irrational number.
A. 38
B. 13.5
C. 625
D. 817

Step: 1
An irrrational number is a number which cannot be written as a quotient of two integers.
Step: 2
625 = 25 and 13.5 = 544
Step: 3
38 is not a perfect square, so 38 cannot be expressed as a quotient of two integers.
Step: 4
And 38 = 6.164414002968..., which is a non-terminating and non-repeating decimal.
Step: 5
So, 38 is an irrational number.
Q9Identify a number that is a rational number but not an integer.

A. 66
B. - 49
C. 20.4
D. - 4.7513...

Step: 1
- 4.7513... is a non-terminating and a non-repeating decimal number, so it is not a rational number.
Step: 2
- 49 = - 7 is a rational number and also an integer.
Step: 3
66 cannot be expressed as a quotient of two integers, so it is not a rational number.
Step: 4
20.4 = 1025 is a rational number, but not an integer.
Q10Identify the irrational number.
A. 310
B. 3
C. 35
D. 36

Step: 1
310 and 35 are rational numbers. Becasue, 310 = 0.3 and 35 = 0.6 , terminating decimals.
Step: 2
36 = 62 = 6, which is a rational number.
[36 is a perfect square.]
Step: 3
3 = 1.732050807568877..., which is a non-terminating and non-repeating decimal.
Step: 4
So, 3 is an irrational number.
Q11Identify the irrational number.
A. 0.98
B. 11
C. 58
D. 111

Step: 1
An irrational number is a non-terminating and non-repeating decimal.
Step: 2
58 = 0.625, 111 = 0.0909091..., are the rational numbers.
Step: 3
0.98 is a terminating decimal.
Step: 4
11 = 3.31662..., which is a non-terminating and non-repeating decimal.
Step: 5
11 is an irrational number.
Q12Identify an irrational number.
A. 817
B. 625
C. 38
D. 13.5

Step: 1
An irrrational number is a number which cannot be written as a quotient of two integers.
Step: 2
625 = 25 and 13.5 = 544
Step: 3
38 is not a perfect square, so 38 cannot be expressed as a quotient of two integers.
Step: 4
And 38 = 6.164414002968..., which is a non-terminating and non-repeating decimal.
Step: 5
So, 38 is an irrational number.