Number System Objective Questions with Answers and Explanations
The concept of Number System MCQs (Class 9) plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Through multiple-choice questions on number systems, Class 9 students can sharpen their problem-solving skills, boost confidence for final exams, and prepare for competitive tests like NTSE and Olympiads.
What Is Number System MCQs (Class 9)?
A Number System MCQ for Class 9 is a multiple-choice question that checks your understanding of different types of numbers (natural, whole, integers, rational, irrational, and real numbers) as well as their properties and conversions. You’ll find this concept applied in areas such as rational/irrational distinctions, decimal representation, and number conversions. Practicing with these MCQs helps Class 9 students develop both accuracy and speed in maths.
Types of Number Systems in Maths
| Number Type | Description | Examples |
|---|---|---|
| Natural Numbers (N) | Counting numbers starting from 1 | 1, 2, 3, 4, ... |
| Whole Numbers (W) | Natural numbers + zero | 0, 1, 2, ... |
| Integers (Z) | Positive and negative whole numbers | ..., -2, -1, 0, 1, 2, ... |
| Rational Numbers (Q) | Numbers that can be written as p/q, q≠0 | 2/3, -5, 0, 1.5 |
| Irrational Numbers | Cannot be written as p/q; non-repeating, non-terminating decimals | √2, π |
| Real Numbers (R) | All rational and irrational numbers | -3, 0, 1.25, √5 |
Key Formula for Number System MCQs (Class 9)
Here’s a standard trick you’ll often use in Number System MCQs:
Checking divisibility, for example: A number is divisible by 3 if the sum of its digits is divisible by 3.
For decimal conversions: To convert fraction p/q to decimal, divide p by q.
Classifying rational/irrational: If the decimal expansion is non-terminating and repeating, it's rational. If non-repeating and non-terminating, it's irrational.
Number System MCQ Preparation Tips
- Read every option carefully before answering.
- Use elimination methods for faster results—cross out obviously wrong choices.
- Remember classification rules for rational and irrational numbers.
- Practice speed calculations—especially with conversions and basic properties.
- Use solved examples from Vedantu for stepwise learning.
Solved Examples: Number System MCQs with Solutions
- Which of the following numbers is irrational?
A. 22/7
B. √3
C. 5
D. -2
Solution:
B. √3 is an irrational number because it cannot be expressed as a simple fraction and its decimal form is non-terminating and non-repeating.
- What is the value of 4√6 + 7√6?
A. 11√6
B. 28√6
C. 10√6
D. 5√36
Solution:
A. 4√6 + 7√6 = (4+7)√6 = 11√6
- If a number can be written as p/q (where q≠0), which type of number is it?
A. Whole
B. Rational
C. Irrational
D. Real
Solution:
B. Any number that can be written as p/q is rational.
- Which of these decimals is a rational number?
A. 3.415926... (non-terminating, non-repeating)
B. 0.333...
C. π
D. √5
Solution:
B. 0.333... is 1/3, a repeating decimal, so it is rational.
- Between which numbers does 17/4 lie?
A. 4 and 5
B. 5 and 6
C. 6 and 7
D. 3 and 4
Solution:
A. 17/4 = 4.25, so it's between 4 and 5.
Extra Practice: MCQ Self-Test
- Identify which of these is a composite number: 2, 3, 4, 5.
- How many even numbers are there between 1 and 10?
- What is the smallest whole number?
- Classify √7 as rational or irrational.
Speed Trick or Vedic Shortcut
Here’s a quick shortcut to check if a 3-digit number is divisible by 11: Add the alternate digits and subtract their sums. If the result is 0 or 11, it’s divisible by 11.
- Example: Is 506 divisible by 11?
5 - 0 + 6 = 11
11 is divisible by 11, so 506 is divisible by 11!
Use speedy checks like these in exams. Vedantu’s live classes offer many more high-speed calculation tips.
Frequent Errors and Misunderstandings
- Confusing rational and irrational numbers—remember, terminating and repeating decimals are rational.
- Forgetting that zero is a whole number.
- Misapplying divisibility rules in haste.
Relation to Other Maths Concepts
The topic of Number System MCQs (Class 9) is closely linked with integer rules, decimal conversions, rational numbers, and prime factorization. Mastering it will help in solving algebra, statistics, and geometry problems as well.
Classroom Tip
A simple mnemonic: “All Lions Roar” stands for All numbers are real, Lions are Rational, Remaining are Irrational. Vedantu teachers often use such phrases to make classification easy to recall in tests.
We explored Number System MCQs (Class 9)—from definitions, types, formulas, mistakes, and how it helps with other maths topics.
Explore More Number System Topics
FAQs on Number System MCQs with Detailed Solutions for Exams
1. What is a number system in Maths?
A number system is a mathematical system used to represent and classify numbers based on specific properties. In Mathematics, numbers are grouped into categories such as:
- Natural numbers (N): 1, 2, 3, ...
- Whole numbers (W): 0, 1, 2, 3, ...
- Integers (Z): ..., −2, −1, 0, 1, 2, ...
- Rational numbers (Q): Numbers of the form p/q (q ≠ 0)
- Irrational numbers: Non-terminating, non-repeating decimals
- Real numbers (R): All rational and irrational numbers
2. What is the difference between rational and irrational numbers?
The key difference is that rational numbers can be written as p/q (q ≠ 0), while irrational numbers cannot be expressed as a fraction.
- Rational numbers have terminating or repeating decimals (e.g., 1/2 = 0.5, 1/3 = 0.333...).
- Irrational numbers have non-terminating, non-repeating decimals (e.g., √2, π).
3. How do you convert a decimal into a fraction?
A decimal is converted into a fraction by writing it over the appropriate power of 10 and simplifying.
- Step 1: Write the decimal without the decimal point as the numerator.
- Step 2: Use 10, 100, 1000, etc., as the denominator based on decimal places.
- Step 3: Simplify the fraction.
4. What are real numbers in the number system?
Real numbers (R) are all numbers that can be represented on the number line, including both rational and irrational numbers.
- Includes integers, fractions, terminating and non-terminating decimals.
- Examples: −3, 0, 5/2, √3, π.
5. What are integers and how are they different from whole numbers?
Integers include positive numbers, negative numbers, and zero, whereas whole numbers include only zero and positive numbers.
- Whole numbers: 0, 1, 2, 3, ...
- Integers: ..., −3, −2, −1, 0, 1, 2, 3, ...
6. How do you identify a terminating and non-terminating decimal?
A terminating decimal ends after a finite number of digits, while a non-terminating decimal continues infinitely.
- Terminating example: 0.25, 1.5
- Non-terminating repeating: 0.333...
- Non-terminating non-repeating: 3.141592...
7. What is the closure property in the number system?
The closure property states that performing an operation on two numbers in a set results in a number from the same set.
- Whole numbers are closed under addition: 2 + 3 = 5.
- Whole numbers are not closed under subtraction: 2 − 5 = −3 (not whole).
8. How do you represent irrational numbers on the number line?
An irrational number is represented on the number line using geometric construction or decimal approximation.
- Example: √2 lies between 1 and 2.
- Its approximate value is 1.414.
- Mark the point at 1.414 on the number line.
9. What is the difference between natural numbers and whole numbers?
The difference is that natural numbers start from 1, while whole numbers include 0.
- Natural numbers: 1, 2, 3, ...
- Whole numbers: 0, 1, 2, 3, ...
10. What types of questions are asked in number system MCQs?
Number system MCQs typically test classification, properties, and operations of numbers. Common question types include:
- Identifying rational and irrational numbers
- Converting decimals to fractions
- Applying properties like closure, commutative, and associative laws
- Finding LCM and HCF
- Determining terminating or non-terminating decimals
