Chapter 1 · Class 9 CBSE · Worksheet

Number Systems Worksheet — Class 9 CBSE Maths

Download a free printable worksheet with 30 questions at 3 difficulty levels. Includes full answer key.

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30 questions (Easy + Medium + Hard) with answer key. Fresh set generated daily.

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Sample Questions — Number Systems

Here are 8 sample questions from this worksheet. Download the full PDF for all 30 questions.

Q1.Which of the following statements is TRUE?

A.Every irrational number is a real number.
B.Every real number is an irrational number.
C.Every rational number is an integer.
D.Every integer is a whole number.

Difficulty: Easy

Q2.Ravi states that the decimal expansion of 7/8 is 0.875, and the decimal expansion of 1/3 is 0.333... (non-terminating repeating). Based on this, he concludes that 7/8 is a rational number and 1/3 is an irrational number. Is Ravi's conclusion correct?

A.Both conclusions are correct.
B.7/8 is rational, but 1/3 is also rational.
C.7/8 is irrational, but 1/3 is rational.
D.Both numbers are irrational.

Difficulty: Easy

Q3.To represent √5 on the number line, a student first draws a right-angled triangle OAB with OA = 2 units and AB = 1 unit, where A is on the x-axis and O is the origin. What is the next logical step?

A.Draw an arc with center A and radius OA to intersect the number line.
B.Draw an arc with center O and radius OB to intersect the number line.
C.Draw an arc with center B and radius AB to intersect the number line.
D.Draw an arc with center O and radius AB to intersect the number line.

Difficulty: Easy

Q4.If 'x' is a rational number and 'y' is an irrational number, which of the following statements is ALWAYS TRUE?

A.x + y is an irrational number.
B.x × y is a rational number.
C.y × y is an irrational number.
D.x / y is a rational number.

Difficulty: Easy

Q5.How many rational numbers can exist between any two distinct rational numbers?

A.Exactly one
B.Exactly two
C.Finitely many
D.Infinitely many

Difficulty: Easy

Q6.A student states: 'The number 0.1010010001... (where the number of zeros increases by one each time) is a rational number because it follows a pattern.' Identify the error in the student's reasoning.

A.The number is indeed rational; there is no error.
B.A rational number must have a repeating block of digits, not just a pattern of increasing zeros.
C.A rational number must have a terminating decimal expansion.
D.The number is an integer, not a rational number.

Difficulty: Easy

Q7.Which of the following correctly describes the set of real numbers?

A.All integers and fractions.
B.All numbers whose square is positive.
C.All numbers that can be written as p/q.
D.The union of rational and irrational numbers.

Difficulty: Easy

Q8.A number whose decimal expansion is non-terminating and non-repeating is classified as a/an _______ number.

A.Irrational
B.Integer
C.Rational
D.Whole

Difficulty: Easy

Answer Key — Sample Questions+
Q1:Every irrational number is a real number.
Q2:7/8 is rational, but 1/3 is also rational.
Q3:Draw an arc with center O and radius OB to intersect the number line.
Q4:x + y is an irrational number.
Q5:Infinitely many
Q6:A rational number must have a repeating block of digits, not just a pattern of increasing zeros.
Q7:The union of rational and irrational numbers.
Q8:Irrational

Download the full PDF for all 30 answers with step-by-step solutions.

About This Worksheet

TopicNumber Systems
BoardCBSE
Class9
Total Questions30 (10 Easy + 10 Medium + 10 Hard)
Answer KeyIncluded
PriceFree

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Frequently Asked Questions

Where can I download a free Number Systems worksheet for Class 9?+
You can download a free Number Systems PDF worksheet for Class 9 CBSE right here on SparkEd. The worksheet includes 30 questions at easy, medium, and hard levels with a complete answer key.
How many questions are in the Number Systems worksheet?+
Each SparkEd worksheet for Number Systems contains 30 questions — 10 easy, 10 medium, and 10 hard. A fresh set is generated daily so you never repeat the same sheet.
Does the Number Systems worksheet include answers?+
Yes. Every SparkEd worksheet comes with a separate answer key so students can self-check their work after completing the sheet.

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