The Class 9 Maths Chapter 3 The World of Numbers Worksheet with Solutions PDF is designed to help students improve their understanding of different types of numbers and their properties through regular practice. This worksheet includes questions based on rational numbers, irrational numbers, decimal expansions, number patterns, prime factorisation, and real-life applications of numbers.
This chapter-wise practice resource helps students revise important concepts in a simple and structured way. Students can use these Worksheets to check their preparation level, strengthen problem-solving skills, and understand how to apply mathematical concepts correctly.
These Class 9 Worksheets are prepared to support concept-based learning and include different question formats for better revision. The Class 9 Maths Worksheets help learners practise step-by-step solutions instead of only memorising formulas. For quick revision, this worksheet provides chapter-focused questions with answers that help students recall important concepts and prepare effectively before exams.
Chapter 3 The World of Numbers Worksheet PDF Download
Students can download the Class 9 Maths Chapter 3 The World of Numbers Worksheet PDF and practise important questions anytime. The worksheet follows a structured approach that allows students to move from basic concepts to advanced problem-solving questions.
The worksheet covers important topics from Chapter 3, including:
- Classification of numbers
- Rational and irrational numbers
- Decimal expansion of numbers
- Finding rational numbers between two numbers
- Prime factorisation
- Number patterns and properties
- Real-life applications of numbers
The The World of Numbers Worksheet PDF includes questions with an answer key to help students verify their solutions and identify topics that need more practice.
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Questions Included in this Worksheet
The Class 9 Maths Chapter 3 The World of Numbers practice worksheet contains concept-based questions arranged from basic understanding to application level. Students should solve these questions first and then check their answers from the answer key given below.
A. Remembering Questions
Q1. Identify whether the following numbers are rational or irrational.
a) 0.454545...
b) √7
c) 5/8
d) 3.14159265...
Q2. Write the prime factorisation of the following numbers.
a) 48
b) 90
Q3. Fill in the blanks.
a) A decimal number that is non-terminating and non-repeating is called a ______ number.
b) A number that can be written in the form p/q, where q ≠ 0, is called a ______ number.
B. Understanding Questions
Q4. Find any three rational numbers between 1/4 and 1/2.
Q5. Convert the repeating decimal 0.777... into the form p/q.
Q6. Explain whether 0.121212... is a rational number or an irrational number. Give a reason.
C. Application Questions
Q7. A rope of length 5/6 metre is joined with another rope of length 3/4 metre. Find the total length of the rope. Also, mention whether the answer is rational or irrational.
Q8. Simplify using number properties:
5/7 × (14/15 + 21/20)
Q9. Observe the number pattern:
2, 3, 5, 7, 11, __, __
Find the next two numbers and explain the pattern.
Answer Key / Solutions
Students can use the Class 9 Maths Chapter 3 The World of Numbers Worksheet with Answers to check their solutions and understand the correct methods.
Answer 1:
a) 0.454545... → Rational number
b) √7 → Irrational number
c) 5/8 → Rational number
d) 3.14159265... → Irrational number
Answer 2:
Prime factorisation:
48 = 2 × 2 × 2 × 2 × 3
= 2⁴ × 3
90 = 2 × 3 × 3 × 5
= 2 × 3² × 5
Answer 3:
a) Irrational number
b) Rational number
Answer 4:
Convert fractions:
1/4 = 4/16
1/2 = 8/16
Three rational numbers between them are:
5/16, 6/16, and 7/16
Answer 5:
Let x = 0.777...
10x = 7.777...
Subtract:
10x − x = 7.777... − 0.777...
9x = 7
x = 7/9
Therefore, 0.777... = 7/9
Answer 6:
0.121212... is a rational number because the digits repeat in a fixed pattern. A repeating decimal can always be written in p/q form.
Answer 7:
Total length:
= 5/6 + 3/4
LCM of 6 and 4 = 12
= 10/12 + 9/12
= 19/12 metre
The answer is a rational number because it can be written as a fraction.
Answer 8:
5/7 × (14/15 + 21/20)
Using distributive property:
= (5/7 × 14/15) + (5/7 × 21/20)
= 2/3 + 3/4
LCM = 12
= 8/12 + 9/12
= 17/12
Answer 9:
Given pattern:
2, 3, 5, 7, 11, __, __
These numbers are prime numbers.
The next two numbers are:
13 and 17
So, the complete pattern is:
2, 3, 5, 7, 11, 13, 17
Skills Developed Through this Worksheet
Practising the NCERT Class 9 Maths Chapter 3 worksheet helps students build important mathematical skills.
Students will learn how to:
- Identify rational and irrational numbers correctly
- Understand different decimal representations
- Convert recurring decimals into fractions
- Apply number properties in calculations
- Solve competency-based Maths questions
- Improve logical thinking and reasoning skills
- Connect number concepts with daily-life examples
Learning Outcomes: After completing this worksheet, students will be able to classify numbers, explain their properties, solve number-based problems, and apply mathematical concepts confidently.
Chapter Revision Checklist
Use this checklist after completing the Class 9 Maths Chapter 3 The World of Numbers practice worksheet.
| Concept | Status |
|---|---|
| I can identify rational numbers | ✓ |
| I can identify irrational numbers | ✓ |
| I understand terminating decimals | ✓ |
| I understand repeating and non-repeating decimals | ✓ |
| I can find rational numbers between two numbers | ✓ |
| I can convert decimals into fractions | ✓ |
| I can solve number pattern questions | ✓ |
| I can apply number concepts in word problems | ✓ |
Students should revise the topics marked incomplete before moving to the next chapter.
