Chapter 1 · Class 9 ICSE · MCQ Test
Rational & Irrational Numbers MCQ Test — Class 9 ICSE
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Rational & Irrational Numbers — MCQ Questions
1Which of the following is a rational number?
Show Answer+
Answer: 3/4
Hint: A rational number can be expressed as p/q where p, q are integers and q is not 0.
Solution:
A rational number is any number that can be written as a fraction p/q, where p and q are integers and q is not zero.
3/4 is already in the form p/q, so it is rational.
sqrt(2), sqrt(3), sqrt(5) are all irrational numbers as they cannot be expressed as fractions.
2Which of the following is an irrational number?
Show Answer+
Answer: sqrt(7)
Hint: An irrational number has a non-terminating, non-repeating decimal expansion.
Solution:
0.75 is rational (= 3/4).
22/7 is rational (it is a fraction).
0.333... is rational (= 1/3, a repeating decimal).
sqrt(7) is irrational because 7 is not a perfect square. — sqrt(7) = 2.6457513...
3The decimal expansion of 1/3 is:
Show Answer+
Answer: 0.333... (non-terminating repeating)
Hint: Divide 1 by 3 using long division.
Solution:
When we divide 1 by 3: — 1 / 3 = 0.3333...
The digit 3 repeats forever, making it a non-terminating repeating decimal.
All non-terminating repeating decimals are rational numbers.
4Which of these represents a terminating decimal?
Show Answer+
Answer: 7/8
Hint: A fraction gives a terminating decimal when its denominator (in lowest terms) has only 2 and 5 as prime factors.
Solution:
For a terminating decimal, the denominator should have only 2 and/or 5 as prime factors.
7/8: denominator 8 = 2 x 2 x 2 (only factor is 2) — 7/8 = 0.875
1/3, 5/6, and 2/9 all have 3 as a factor in the denominator, so they are non-terminating.
5Simplify: sqrt(9)
Show Answer+
Answer: 3
Hint: Find which number multiplied by itself gives 9.
Solution:
We need to find x such that x^2 = 9.
Since 3 x 3 = 9: — sqrt(9) = 3
6Between which two consecutive integers does sqrt(10) lie?
Show Answer+
Answer: 3 and 4
Hint: Find which perfect squares are closest to 10.
Solution:
We know that 3^2 = 9 and 4^2 = 16.
Since 9 < 10 < 16: — 3 < sqrt(10) < 4
So sqrt(10) lies between 3 and 4.
7The number 0 is:
Show Answer+
Answer: Only rational
Hint: Can 0 be written as p/q where q is not zero?
Solution:
0 can be written as 0/1, which is in the form p/q.
Since p = 0 and q = 1 are both integers and q is not zero, 0 is rational.
8Which statement is true about the sum of two rational numbers?
Show Answer+
Answer: Always rational
Hint: Think about adding two fractions.
Solution:
If a/b and c/d are two rational numbers, their sum is: — (ad + bc) / bd
Since ad + bc is an integer and bd is a non-zero integer, the result is rational.
The sum of two rational numbers is always rational.
9pi (pi) is:
Show Answer+
Answer: An irrational number
Hint: Is 22/7 the exact value of pi?
Solution:
pi = 3.14159265... is a non-terminating, non-repeating decimal.
22/7 is only an approximation of pi, not its exact value.
Since pi cannot be expressed as a fraction of integers, it is irrational.
10Express 0.6666... as a fraction.
Show Answer+
Answer: 2/3
Hint: Let x = 0.666... and multiply both sides by 10.
Solution:
Let x = 0.6666...
Multiply by 10: — 10x = 6.6666...
Subtract: — 10x - x = 6.6666... - 0.6666...
Solve: — 9x = 6, so x = 6/9 = 2/3
Want more questions?
Practice 60+ questions with AI-powered doubt clearing and step-by-step solutions.
Tips for Rational & Irrational Numbers MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Rational & Irrational Numbers MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
Master Rational & Irrational Numbers on SparkEd
Go beyond MCQs. Practice at three difficulty levels with instant feedback, solutions, and an AI coach to clear every doubt.
Start PractisingSparkEd Maths offers free MCQ tests for Class 1-10 across 7 education boards. All questions are aligned to the 2025-26 syllabus with step-by-step solutions and AI-powered doubt clearing.