Are these practice questions for The World of Numbers based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 9 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for The World of Numbers free?

Yes. Every chapter includes free practice questions for Class 9 students to get you started.

What types of questions are included?

The practice set for The World of Numbers mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for The World of Numbers for full coverage.

How many practice questions are there for The World of Numbers?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

The World of Numbers Class 9 Mathematics Practice Questions with Answers

easy

Evaluate the claim: 'Any number with a non-terminating decimal expansion is an irrational number.' Justify your evaluation with a counter-example and formulate a corrected, precise statement.

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easy

Apply the averaging method once to find a rational number that lies exactly between

\frac{2}{7}

and

\frac{3}{7}

.

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easy

List two famous examples of irrational numbers.

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easy

Critique the common misconception that the number

0.999...

is 'infinitely close but not equal' to 1. Formulate a definitive mathematical conclusion.

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easy

Define the set of Natural Numbers and state the symbol used to represent it.

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easy

Solve for

x

by converting the repeating decimal

x = 0.\overline{54}

into a rational number of the form

\frac{p}{q}

.

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easy

Summarize Brahmagupta's three fundamental rules for arithmetic operations involving zero (śhūnya).

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easy

Name the Indian mathematician who formally defined zero as a number and laid down its arithmetic rules.

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easy

A submarine is at a depth of 250 meters below sea level. It then ascends 75 meters. Calculate its new position relative to sea level, representing the depth as an integer.

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easy

Analyze the number

\sqrt{144} - \sqrt{14}

. Classify it as rational or irrational and provide a reason for your answer.

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easy

Justify why, in the definition of a rational number

\frac{p}{q}

, the condition

q \neq 0

is critically important.

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easy

Convert the decimal

0.225

into a rational number of the form

\frac{p}{q}

in its simplest form.

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medium

Justify why the sum of a rational number and an irrational number must always be irrational.

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medium

Without performing long division, analyze the fraction

\frac{17}{80}

to determine if its decimal expansion is terminating or non-terminating repeating. Justify your answer.

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medium

Apply the standard method to convert the mixed repeating decimal

2.1\overline{3}

into a rational number of the form

\frac{p}{q}

.

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medium

Formulate a concise argument to prove that for any two distinct rational numbers

a

and

b

with

a < b

, their average,

m = \frac{a+b}{2}

, is a rational number that lies strictly between them.

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medium

Calculate the value of the following expression:

|-8| - |\frac{5}{2} - 4| + |0 - 3|

.

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medium

Describe the 'density' property of rational numbers.

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medium

Critique the following flawed 'proof' that a student wrote to show

\sqrt{5}

is irrational: 'Assume

\sqrt{5}

is rational, so

\frac{p}{q} = \sqrt{5}

. But we know

\sqrt{5}

is irrational, so a rational number cannot equal an irrational number. This is a contradiction, so

\sqrt{5}

must be irrational.' Justify why this reasoning is invalid.

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medium

Demonstrate how to locate

\sqrt{5}

on the number line using a compass and straightedge. Describe the key steps of your construction based on the Baudhāyana-Pythagoras Theorem.

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medium

Design a formal proof by contradiction to demonstrate that the number

3\sqrt{2} - 5

is irrational, given that

\sqrt{2}

is known to be irrational. Justify each logical step in your proof.

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medium

Describe the historical significance of the Lebombo Bone as evidence for early mathematical thought.

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medium

Create a fraction in the form

\frac{p}{q}

that is equivalent to the decimal

2.1\overline{35}

. Formulate the algebraic steps required to justify your conversion process.

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medium

Explain the difference between a rational number and an irrational number based on their decimal expansions.

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medium

Describe the five main sets of numbers in the order of their evolution: Natural, Integers, Rational, Irrational, and Real. For each set, explain what it includes and how it extends the previous set.

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medium

A right-angled triangle has its two shorter sides measuring

a = \sqrt{3}

cm and

b = \sqrt{6}

cm. (a) Calculate the length of the hypotenuse,

c

. (b) Calculate the perimeter of the triangle. (c) Analyze the perimeter and classify it as a rational or irrational number.

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medium

A baker uses

\frac{3}{8}

of a sack of flour for a batch of bread. He then uses

\frac{1}{3}

of the remaining flour for pastries. If the sack initially contained 24 kg of flour, calculate the weight of flour left in the sack.

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medium

What is the absolute value of a rational number? Recall the absolute value of

-\frac{5}{3}

.

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medium

Apply the method of common denominators to find four distinct rational numbers that lie between

\frac{3}{5}

and

\frac{2}{3}

.

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medium

Propose a simple test to determine if a rational number

\frac{p}{q}

(in its simplest form) will have a terminating decimal expansion, without performing the actual division. Justify your proposal.

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medium

Identify the set of numbers that is formed by combining all rational and all irrational numbers.

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medium

A shopkeeper starts a month with a debt of ₹5000. In the first week, he makes a profit of ₹3500. In the second week, he incurs a loss of ₹2200. In the third week, he takes another loan of ₹1500 to buy stock. In the final week, he makes a profit of ₹4800. Analyze his transactions using integers and calculate his final financial standing (fortune or debt) at the end of the month.

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hard

Summarize how the Indian philosophical concept of Śhūnyatā contributed to the mathematical invention of zero.

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hard

Design a geometric construction using only a ruler and compass to create a line segment of length

\sqrt{6}

units on a number line. Justify the steps of your design using the Baudhāyana-Pythagoras Theorem.

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hard

Explain the logic of 'Proof by Contradiction' by summarizing the main steps used to demonstrate that

\sqrt{2}

is irrational. You do not need to write out the full mathematical proof, but describe the purpose of each logical step.

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hard

Explain the relationship between the sets of numbers represented by the symbols

\mathbb{N}

,

\mathbb{Z}

, and

\mathbb{Q}

.

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hard

Evaluate the statement: 'The square root of any prime number is an irrational number.' Justify your evaluation.

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hard

Examine the number

x = 5.10110111011110...

. (a) Is this number rational or irrational? Justify your answer by analyzing its decimal expansion. (b) Find two distinct rational numbers that lie between

5.101

and

x

.

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hard

Describe the two types of repeating decimals and explain the general method for converting each type into the form

\frac{p}{q}

.

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hard

The text presents the evolution of numbers as a linear progression from Natural numbers to Integers to Rationals to Reals, each created to solve a deficit in the previous set. Critique this simplified model. Propose a more nuanced perspective on the historical development of number systems, justifying your proposal with at least two pieces of evidence from the source text.

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hard

Justify Brahmagupta's rule that 'the product of two debts is a fortune' (i.e., a negative number times a negative number is a positive number) by creating a proof that relies on the distributive law and the property of zero.

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hard

Explain the concept of 'closure' for a set of numbers under an operation. State whether the set of Integers (

\mathbb{Z}

) is closed under division and provide an example.

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hard

Propose a method for finding an irrational number that lies strictly between any two distinct rational numbers,

a

and

b

. Justify why your proposed number is both irrational and lies between

a

and

b

.

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hard

Formulate a general method to find any number of 'n' distinct rational numbers between two given rational numbers

\frac{p}{q}

and

\frac{r}{s}

. Justify your method and use it to create 4 distinct rational numbers between

\frac{2}{5}

and

\frac{3}{4}

.

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hard

Let

a = 0.\overline{3}

and

b = 0.\overline{15}

. Calculate the value of

a+b

. Express the final answer as a fraction in the form

\frac{p}{q}

and also as a repeating decimal.

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The World of NumbersClass 9 Mathematics Practice Questions