Mathematics
Class 9
Rational and Irrational Numbers - Class 9 Worksheet
Sort, spot and solve - number system practice for Class 9
Four activities to check whether you can tell a rational number from an irrational one, work with decimal expansions, and justify your answers the way an exam wants.
Fill in the Blanks
Warm-up: Fill in the Blanks
Complete each sentence using a word from the box below.
1.A number that can be written in the form p/q, where q is not , is called a rational number.
2.The decimal expansion of an irrational number is and non-repeating.
3.pi and root 2 are examples of numbers.
4.A number has a decimal expansion that either ends or repeats.
5.0.3333... is an example of a decimal, so it is rational.
Quiz (MCQ)
Multiple Choice Questions
Circle the correct option for each question.
1. Which of these is an irrational number?
2. What is the decimal expansion of 7/8?
3. Between any two rational numbers, how many irrational numbers can be found?
4. Which of the following is a rational number?
5. The sum of a rational number and an irrational number is always:
6. Which number lies between 0 and 1 and is rational?
True / False
True or False?
Write True or False for each statement. Be ready to explain your reasoning if asked.
1. Every integer is a rational number.
2. Every rational number is an integer.
3. The number 0 is neither rational nor irrational.
4. root 4 is an irrational number.
5. pi is exactly equal to 22/7.
6. The product of two irrational numbers is always irrational.
7. Every terminating decimal represents a rational number.
8. There are infinitely many rational numbers between any two given rational numbers.
Short Answer
Explain It Yourself
Answer in your own words. Show any working where needed.
1. A classmate says 'root 16 must be irrational because it has a root sign.' Explain why this is wrong, with the correct answer.
2. Write the decimal expansion of 1/3 and 2/7. Which one, if any, terminates? Explain what this tells you about their type of number.
3. Find one rational and one irrational number that lie between 2 and 3, and briefly explain how you found each one.
4. Why does 0.101001000100001... (a pattern that never settles into a repeating block) count as an irrational number?
These are open-ended - there's no single right answer to check.
Written by Lernizy Editorial Team
Updated 27 Aug 2026