The World of Numbers Class 9 Maths Worksheet with Quiz and Activities
Classify rational and irrational numbers, convert decimals and fractions and build the square root spiral in 2D and 3D. On WitKnowLearn you get the The World of Numbers Class 9 online quiz, online activities and interactive games, a number lab, a virtual lab and a worksheet-style practice sheet for NCERT Ganita Manjari Chapter 3.
The World of Numbers Class 9 Online Quiz
20 questions: 10 easy, 5 average and 5 thinking. Tap an answer and the next question comes up.
The World of Numbers Class 9 Activities
👆 Tap a tab to switch: Learn, Games, Labs, Challenges, Virtual Lab and Practice sheet
The World of Numbers: the Journey of Numbers Story
A short read for Class 9 before you play. These notes follow Chapter 3 of NCERT Ganita Manjari, Part I.
0️⃣ The revolution of Shunya
Zero began as a gap and became a number. Indian mathematicians such as Brahmagupta gave clear rules for adding, subtracting and multiplying with zero and with negative numbers.
➖ Integers and debts
Negative numbers describe debts and low temperatures. A debt taken away from a debt gives a fortune, so (-8) x (-7) = 56.
🍰 Fractions and rational numbers
Fractions fill the spaces between integers. Between any two rational numbers there is another one, so they are packed densely on the number line.
📏 Irrational numbers
The diagonal of a unit square is the square root of 2, and it cannot be written as p/q. Its decimal never ends and never repeats.
🌀 The square root spiral
Build right triangles one after another and every hypotenuse is a square root: 2, 3, 4, 5 and so on under the root sign.
🔁 Cyclic decimals
The decimals of the sevenths use the same six digits, 142857, in the same cyclic order.
The World of Numbers Class 9 Activities
Classify, convert and construct on the Number Train. Earn up to 3 stars in every activity.
This page follows NCERT Class 9 Maths Ganita Manjari, Part I, Chapter 3. Students work with integers, rational numbers, decimal expansions, irrational numbers and the square root spiral.
The activities are pitched at Class 9 level. Students sort decimals by type, pop true facts, match terms, convert repeating decimals to fractions, test closure, and build the square root spiral in a 2D and 3D view. Explore more Class 9 maths worksheets on WitKnowLearn after this chapter.
Formulas and facts to know
| Type of number | Decimal expansion | Example |
|---|---|---|
| Integer | Ends at once | -5 |
| Rational | Terminates or repeats | 3/8 = 0.375 |
| Rational | Repeats | 2/3 = 0.666... |
| Irrational | Never ends, never repeats | √2 = 1.41421... |
How to use this page
- Flip the six cards and try the Number Lab in the Learn tab.
- Play the five games and the five labs to practise each idea.
- Finish the five challenges to collect up to 15 points.
- Build the square root spiral in the Virtual Lab and look at it in 2D and 3D.
- Take the 20-question online quiz, with assertion and reason and case study questions, and fill in the practice sheet.
Worked examples
10x = 4.555..., 100x = 45.555..., so 90x = 41 and x = 41/90.
(1/4 + 1/3)/2 = 7/24.
Face diagonal √2, then √(2 + 1) = √3.
This The World of Numbers worksheet for Class 9 maths gives you online activities and interactive games that make numbers clear. Every activity has a goal, a hint and a short fact, so students learn while they enjoy.
Complete Guide: NCERT Class 9 Maths The World of Numbers Chapter 3
This guide is for Class 9 students, parents and teachers. It covers Chapter 3 of NCERT Ganita Manjari, Part I, and shows how to use the quiz, labs and games on this page.
Introduction to The World of Numbers
The chapter follows the growth of numbers from zero and integers to fractions, irrational numbers and the real numbers, with decimal expansions and patterns on the way.
What is there in this chapter
- The revolution of Shunya and zero.
- Integers and the laws of Brahmagupta.
- Fractions and rational numbers.
- Rational numbers between two numbers.
- Irrational numbers and the square root spiral.
- Real numbers, decimals and cyclic patterns.
Learning objectives
- Classify numbers as integers, rational or irrational.
- Convert between fractions and decimal expansions.
- Find rational numbers between two numbers.
- Prove that a number is irrational by contradiction.
- Reason with assertions and case studies.
Learning outcomes
- The student can write 0.4555... as 41/90.
- The student can state that 7/40 terminates and 4/15 repeats.
- The student can find that the 6th hypotenuse of the spiral is the square root of 7.
- The student can solve a case study on the diagonal of a cube.
The World of Numbers Class 9 resources on this page
| Resource | What it gives |
|---|---|
| Online quiz | 20 questions: 10 easy, 5 average and 5 thinking, with assertion and reason and case study questions and a full review |
| Flip cards | 6 picture cards with one-line rules |
| Number Lab | A hands-on lab with 3 rounds |
| Games | 5 interactive games |
| Labs | 5 activity labs |
| Virtual Lab | 2 experiments and a 2D and 3D spiral builder with aim, procedure, observations and conclusion |
| Challenges | 5 challenges, 15 points in all |
| Practice sheet | A worksheet-style sheet with 16 questions, name and date lines and a live score |
Key facts
| Idea | Rule |
|---|---|
| Rational | Can be written as p/q |
| Terminating | Denominator has only 2 and 5 |
| Repeating to p/q | Use x, 10x or 100x and subtract |
| Between two numbers | Take the average |
| Irrational | Never ends and never repeats |
| Closure | One counterexample breaks it |
Types of questions you may see
- Classify a number as rational or irrational.
- Convert a repeating decimal to p/q.
- Find rational numbers between two numbers.
- Prove that a root is irrational.
- Assertion and reason questions.
- Case studies on spirals, ribbons and temperatures.
Solved examples
99x = 63, so x = 7/11.
(21/2) ÷ (3/4) = 14 pieces.
50 = 8 x 6 + 2, so it is the 2nd digit of 142857, which is 4.
1.5, because 1.52 = 2.25 lies between 2 and 3.
√25 = 5, so 24 triangles give exactly 5 units.
√(4 + 4 + 4) = √12.
Common mistakes
| Mistake | Correct idea |
|---|---|
| Thinking the square root of every number is irrational. | The square root of a perfect square is a whole number. |
| Calling 0.333... irrational. | It repeats, so it equals 1/3 and is rational. |
| Testing an unreduced fraction. | Reduce first, then factorise the denominator. |
| Saying the product of irrationals is irrational. | The square root of 2 times itself is 2. |
| Sign errors with negatives. | Negative times negative is positive. |
The World of Numbers in daily life
Measuring, money, temperature and computer screens all use numbers from this chapter. Square roots appear when we find diagonals and distances.
Tips for parents and teachers
- Use graph paper to build the square root spiral.
- Divide 1 by 7 by hand and spot the cycle.
- Ask students to find three rational numbers between two fractions.
- Practise one assertion and one case study each week.
Related Class 9 Maths Worksheets
- 🔢Number Systems Class 9 Worksheet
- 🧮Polynomials Class 9 Worksheet
- 📍Coordinate Geometry Class 9 Worksheet
- 📈Linear Equations in Two Variables Class 9
- 📐Introduction to Euclids Geometry Class 9
- 📏Lines and Angles Class 9 Worksheet
- 🔺Triangles Class 9 Worksheet with MCQs
- 🔷Quadrilaterals Class 9 Worksheet
- ⭕Circles Class 9 Worksheet with MCQs
- 🧩Herons Formula Class 9 Worksheet
- 📦Surface Area and Volumes Class 9 Worksheet
- 📊Statistics Class 9 Worksheet
The World of Numbers Class 9 FAQs
What is Chapter 3 of NCERT Class 9 Maths Ganita Manjari?
Chapter 3 is The World of Numbers. It covers the revolution of zero, integers and Brahmagupta rules, fractions and rational numbers, irrational numbers, and real numbers with their decimal expansions and cyclic patterns.
What is a rational number?
A rational number is a number that can be written as p/q, where p and q are integers and q is not 0. Integers, fractions and terminating or repeating decimals are all rational.
What is an irrational number?
An irrational number cannot be written as p/q. Its decimal expansion never ends and never repeats. Examples are the square root of 2, the square root of 3 and the square root of 10.
How do you know if a fraction has a terminating decimal?
Write the fraction in lowest terms and factorise the denominator. If it has no prime factor other than 2 and 5, the decimal terminates. For example 7/40 = 0.175 terminates, but 4/15 repeats.
How do you convert a repeating decimal to a fraction?
Let x be the decimal, multiply by 10 or 100 to line up the repeating blocks, subtract, and solve. For x = 0.2727..., 100x - x = 27, so x = 27/99 = 3/11.
Is 0.999... equal to 1?
Yes. Let x = 0.999... Then 10x = 9.999..., so 9x = 9 and x = 1. The two are different names for the same number.
How do you find rational numbers between two numbers?
The average of two rational numbers lies between them. Between 1/4 and 1/3 the average is 7/24. You can repeat this to find as many as you like, so there are infinitely many.
How do you prove that the square root of 5 is irrational?
Assume it equals p/q in lowest terms. Squaring gives p^2 = 5q^2, so 5 divides p. Writing p = 5k gives q^2 = 5k^2, so 5 divides q. This contradicts lowest terms, so the square root of 5 is irrational.
What is the square root spiral?
It is a spiral of right triangles. Each triangle has one leg of 1 unit and another leg equal to the last hypotenuse. The nth hypotenuse is the square root of n + 1.
What are Brahmagupta rules for negative numbers?
Debt times debt is a fortune, so (-a) x (-b) = ab. Taking away a debt adds, so a - (-b) = a + b. A negative divided by a negative is positive.
Why is 1/7 a cyclic decimal?
Dividing 1 by 7 gives remainders 3, 2, 6, 4, 5, 1 and then repeats, so 1/7 = 0.142857142857... The other sevenths use the same six digits starting at a different place.
What can students do on this page?
Students can take a 20-question online quiz with assertion and reason and case study questions, play five games, try five online activities, finish five challenges, run the Number Lab, do two virtual experiments, build the square root spiral in 2D and 3D, and fill in a 16-question practice sheet with a Show answers button.
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