Class 9 Maths Number System MCQs with Answer

Class 9 Maths Number System MCQs: Understanding the basics of the number system is very important for students of Class 9, as it builds a strong base for higher mathematics. This section on Class 9 Maths Number System MCQs with Answer is designed to help students practice key concepts in a simple and clear way. These questions follow the latest syllabus of the CBSE Board and are useful for both school exams and competitive preparation.

The number system class 9 mcq set includes questions on rational numbers, irrational numbers, real numbers, and their properties. Students can also explore class 9 maths chapter 1 mcq with answers to check their understanding and improve problem-solving skills. Regular practice of number system mcq class 9 helps in reducing calculation mistakes and increases confidence step by step.

In addition, learners can try a class 9 maths chapter 1 mcq online test to test their speed and accuracy. These MCQs are based on concepts like decimal expansion, laws of exponents, and representation of numbers on the number line. Sometimes students feel this chapter is easy, but small confusion can happen if concepts are not clear properly. So, practicing regularly is really helpful for better results.

What is Number System MCQ Class 9?

Number System MCQs for Class 9 Maths are multiple-choice questions that test your basic understanding of numbers and their types. These questions are an important part of Class 9 Maths Chapter 1 MCQs with answers and help students prepare better for exams.

In these questions, students learn about different types of numbers such as natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. You will also practice topics like decimal representation, number conversion, and identifying rational and irrational numbers.

Regular practice of number system MCQ class 9 improves speed, accuracy, and confidence. It also helps students perform well in CBSE Board exams and online tests.

Types of Number Systems in Maths

This table is very helpful for solving class 9 maths chapter 1 mcq online test questions quickly.

Important Tricks for Number System MCQs (Class 9)

Here are some easy rules used in number system class 9 mcq questions:

• Divisibility Rule: A number is divisible by 3 if the sum of its digits is divisible by 3.
• Fraction to Decimal: To convert p/q into decimal, simply divide p by q.
• Rational Numbers: Decimal is terminating or repeating
• Irrational Numbers: Decimal is non-terminating and non-repeating

These tricks are very useful in solving class 9 maths number system MCQs with answers.

Q. Which of the following statements is TRUE regarding the sum of a rational number and an irrational number?

1. The sum is always rational.
2. The sum is always irrational.
3. The sum can be rational or irrational depending on the numbers.
4. The sum is always an integer.

Answer: B

Explanation:

Let 'q' be a rational number and 'i' be an irrational number. Assume, for contradiction, that q + i = r, where 'r' is a rational number. Then i = r - q. Since the difference of two rational numbers is rational, this would imply that 'i' is rational, which contradicts our initial assumption that 'i' is irrational. Therefore, the sum must be irrational.

Q. Consider the number 0.12112111211112... What type of decimal expansion does this number have?

1. Terminating decimal
2. Non-terminating recurring decimal
3. Non-terminating non-recurring decimal
4. Terminating recurring decimal

Answer: C

Explanation:

A non-terminating non-recurring decimal expansion is characteristic of an irrational number. In this sequence, the pattern of '1's between '2's increases (one '1', then two '1's, then three '1's, and so on), meaning there is no repeating block of digits. Therefore, it does not terminate and does not recur.

Q. Simplify the expression: (23)2 × 2-4

1. 22
2. 2-2
3. 210
4. 2-1

Answer: A

Explanation:

Using the laws of exponents: (am)n = amn and am × an = am+n. First, (23)2 = 23×2 = 26. Then, 26 × 2-4 = 26 + (-4) = 26 - 4 = 22.

Q. Which of the following is equivalent to 3√27 × 2√64?

1. 12
2. 24
3. 36
4. 48

Answer: B

Explanation:

First, calculate the cube root of 27: 3√27 = 3 (since 33 = 27). Next, calculate the square root of 64: 2√64 = 8 (since 82 = 64). Finally, multiply the results: 3 × 8 = 24.

Q. Which point on the number line best represents √10?

1. A point between 2 and 3, closer to 2.
2. A point between 3 and 4, closer to 3.
3. A point exactly at 3.16.
4. A point between 3 and 4, closer to 4.

Answer: B

Explanation:

We know that 32 = 9 and 42 = 16. Since 9 < 10 < 16, it follows that √9 < √10 < √16, which means 3 < √10 < 4. To determine if it's closer to 3 or 4, we can observe that 10 is much closer to 9 than it is to 16. Specifically, 10 - 9 = 1, while 16 - 10 = 6. Thus, √10 is closer to 3.

Q. How many rational numbers exist between any two distinct rational numbers?

1. Exactly one
2. A finite number (more than one)
3. Infinitely many
4. Zero

Answer: C

Explanation:

This property is known as the density property of rational numbers. Given any two distinct rational numbers, say 'a' and 'b' where a < b, we can always find another rational number (a+b)/2 between them. We can repeat this process infinitely, demonstrating that there are infinitely many rational numbers between any two distinct rational numbers.

Q. Express 0.0000000085 in standard exponential form (scientific notation).

1. 8.5 × 10-8
2. 8.5 × 10-9
3. 8.5 × 108
4. 8.5 × 109

Answer: B

Explanation:

To express a number in scientific notation, we move the decimal point until there is only one non-zero digit to its left. In 0.0000000085, we move the decimal point 9 places to the right to get 8.5. Since we moved the decimal to the right, the exponent will be negative. Therefore, it is 8.5 × 10-9.

Q. Which of the following statements is always TRUE about the product of two irrational numbers?

The product is always irrational.

The product is always rational.

The product can be rational or irrational.

The product is always an integer.

Answer: C

Explanation:

Consider these examples:
1. √2 is irrational, and √3 is irrational. Their product is √6, which is irrational.
2. √2 is irrational, and √2 is irrational. Their product is (√2)2 = 2, which is rational.
Since we have examples where the product is irrational and where it is rational, the product can be either.

Q. Convert the recurring decimal 0.‾47 (where ‾47 means 47 repeats) into a fraction in its simplest form.

1. 47/100
2. 47/99
3. 47/90
4. 47/999

Answer: B

Explanation:

Let x = 0.‾47 = 0.474747... (Equation 1)
Since two digits are repeating, multiply by 100:
100x = 47.474747... (Equation 2)
Subtract Equation 1 from Equation 2:
100x - x = 47.474747... - 0.474747...
99x = 47
x = 47/99
This fraction is already in its simplest form as 47 is a prime number and 99 is not a multiple of 47.

Q. How many integers lie between √3 and √26?

1. 2
2. 3
3. 4
4. 5

Answer: C

Explanation:

First, approximate the values of √3 and √26.
√3 is approximately 1.732 (since 12 = 1 and 22 = 4, √3 is between 1 and 2).
√26 is approximately 5.099 (since 52 = 25 and 62 = 36, √26 is between 5 and 6, very close to 5).
The integers greater than 1.732 and less than 5.099 are 2, 3, 4, and 5. There are 4 such integers.

Q. If (1/3)-2 × 3x = 35, what is the value of x?

1. 1
2. 2
3. 3
4. 4

Answer: C

Explanation:

We use the law of exponents (a/b)-n = (b/a)n and am × an = am+n.
(1/3)-2 = (3/1)2 = 32.
So the equation becomes: 32 × 3x = 35.
32+x = 35.
Equating the exponents, we get: 2 + x = 5.
x = 5 - 2 = 3.

Q. Simplify: √75 - √12

1. √63
2. 3√3
3. 7√3
4. 4√3

Answer: B

Explanation:

To simplify, we find perfect square factors of each number under the radical.
√75 = √(25 × 3) = √25 × √3 = 5√3.
√12 = √(4 × 3) = √4 × √3 = 2√3.
Now substitute these simplified forms back into the expression:
5√3 - 2√3 = (5 - 2)√3 = 3√3.

Q. Which of the following numbers is irrational?

1. √225
2. 0.3796
3. 7.478478...
4. 0.1010010001…

Answer: D

Explanation:

Let's analyze each option:
1. √225 = 15, which is an integer and thus rational.
2. 0.3796 is a terminating decimal, which can be written as 3796/10000, so it is rational.
3. 7.478478... is a non-terminating recurring decimal (478 repeats), which can be expressed as a fraction, so it is rational.
4. 0.1010010001... is a non-terminating non-recurring decimal, as the number of zeros between the ones increases, indicating no repeating block. Therefore, it is irrational.

Q. Evaluate (51/2 × 51/3) / 51/6

1. 51/5
2. 52/3
3. 52/6
4. 51

Answer: B

Explanation:

Using the laws of exponents: am × an = am+n and am / an = am-n.
First, simplify the numerator: 51/2 × 51/3 = 5(1/2) + (1/3) = 5(3/6) + (2/6) = 55/6.
Now, divide by 51/6: 55/6 / 51/6 = 5(5/6) - (1/6) = 54/6.
Simplify the exponent: 4/6 = 2/3.
So the final answer is 52/3.

Q. To represent √5 on a number line, which geometric construction is typically used?

1. Drawing a circle with radius 5.
2. Constructing a right-angled triangle with sides 1 and 2.
3. Finding the midpoint of the segment from 0 to 5.
4. Using a ruler to measure 2.23 units.

Answer: B

Explanation:

According to the Pythagorean theorem, if a right-angled triangle has perpendicular sides of length 'a' and 'b', then the hypotenuse 'c' has length √(a2 + b2). For √5, we can choose a=1 and b=2. Then c = √(12 + 22) = √(1 + 4) = √5. One would construct this triangle on the number line (e.g., from 0 to 2 on the x-axis, and 1 unit up on the y-axis) and then use a compass to transfer the length of the hypotenuse to the number line.

Q. If x = 0.‾3 + 0.‾4, what is x in p/q form?

1. 7/9
2. 7/10
3. 7/99
4. 7/100

Answer: A

Explanation:

First, convert each recurring decimal to a fraction:
Let a = 0.‾3. Then 10a = 3.‾3. Subtracting, 9a = 3, so a = 3/9 = 1/3.
Let b = 0.‾4. Then 10b = 4.‾4. Subtracting, 9b = 4, so b = 4/9.
Now, x = a + b = 1/3 + 4/9.
To add, find a common denominator: x = 3/9 + 4/9 = 7/9.

Q. Multiply and simplify: (√5 + √2) (√5 - √2)

1. 7
2. 3
3. √10
4. 7 - 2√10

Answer: B

Explanation:

This expression is in the form (a + b)(a - b) = a2 - b2.
Here, a = √5 and b = √2.
So, (√5 + √2) (√5 - √2) = (√5)2 - (√2)2
= 5 - 2
= 3.

Q. If 81x = 1/9, what is the value of x?

1. -1/2
2. 1/2
3. -2
4. 2

Answer: A

Explanation:

We need to express both sides of the equation with the same base. Both 81 and 9 can be expressed as powers of 3.
81 = 34
1/9 = 9-1 = (32)-1 = 3-2
So the equation becomes: (34)x = 3-2
34x = 3-2
Equating the exponents: 4x = -2
x = -2/4 = -1/2.

Q. Which of the following statements correctly defines a Real Number?

1. Any number that can be written as a fraction p/q where q ≠ 0.
2. Any number that can be represented on a number line.
3. Any number that is either a natural number or a whole number.
4. Any number whose decimal expansion is terminating.

Answer: B

Explanation:

Real numbers encompass all rational and irrational numbers. Rational numbers are those that can be expressed as a fraction p/q (option 1), and their decimal expansions are either terminating or non-terminating recurring. Irrational numbers cannot be expressed as a fraction and have non-terminating non-recurring decimal expansions. Both rational and irrational numbers can be uniquely located on a number line, making option 2 the most comprehensive and correct definition of a real number.

Q. Insert two irrational numbers between 2 and 2.5.

1. √3 and √4
2. √4.5 and √6
3. 2.1010010001... and 2.3030030003...
4. 2.1 and 2.4

Answer: C

Explanation:

For numbers to be irrational, they must have non-terminating, non-recurring decimal expansions. Also, they must lie strictly between 2 and 2.5.
1. √3 ≈ 1.732 (not between 2 and 2.5); √4 = 2 (not strictly between).

2. √4.5 ≈ 2.12 (between); √6 ≈ 2.45 (between). This option gives two irrational numbers that fit the criteria. However, option 3 provides a more explicit construction of irrational numbers.

3. 2.1010010001... is clearly non-terminating and non-recurring, and it's greater than 2 and less than 2.5. Similarly, 2.3030030003... is also irrational and falls within the range. This is a standard way to construct irrational numbers.

4. 2.1 and 2.4 are terminating decimals, thus rational.

Q. Without actual division, determine the type of decimal expansion for 13/3125.

1. Terminating
2. Non-terminating recurring
3. Non-terminating non-recurring
4. Cannot be determined without division

Answer: A

Explanation:

A rational number p/q (where p and q are co-prime) has a terminating decimal expansion if and only if the prime factorization of the denominator q is of the form 2m × 5n, where m and n are non-negative integers.
Here, the denominator is 3125.
Let's find the prime factors of 3125: 3125 = 5 × 625 = 5 × 5 × 125 = 5 × 5 × 5 × 25 = 5 × 5 × 5 × 5 × 5 = 55.
Since the denominator is of the form 20 × 55, the decimal expansion is terminating.

Q. Simplify the expression: (√11 - √7)2

1. 18 - 2√77
2. 4
3. 18
4. 11 - 7

Answer: A

Explanation:

We use the algebraic identity (a - b)2 = a2 - 2ab + b2.
Here, a = √11 and b = √7.
( √11 - √7)2 = (√11)2 - 2(√11)(√7) + (√7)2
= 11 - 2√(11 × 7) + 7
= 11 - 2√77 + 7
= (11 + 7) - 2√77
= 18 - 2√77.

Q. What is the value of (256)0.16 × (256)0.09?

1. 4
2. 16
3. 64
4. 256

Answer: A

Explanation:

Using the law of exponents am × an = am+n:
(256)0.16 × (256)0.09 = (256)0.16 + 0.09
= (256)0.25
Convert the decimal exponent to a fraction: 0.25 = 1/4.
= (256)1/4
This means the fourth root of 256. We know that 44 = 4 × 4 × 4 × 4 = 16 × 16 = 256.
Therefore, (256)1/4 = 4.

Q. Rationalize the denominator of 1 / (√3 + √2 - √5).

1. (3√2 + 2√3 + √30) / 12
2. (3√2 - 2√3 - √30) / 12
3. (3√2 + 2√3 - √30) / 12
4. (3√2 - 2√3 + √30) / 12

Answer: A

Explanation:

Let the expression be 1 / (√3 + √2 - √5). Group the terms in the denominator: 1 / [(√3 + √2) - √5].
Multiply by the conjugate [(√3 + √2) + √5] / [(√3 + √2) + √5]:
Numerator = √3 + √2 + √5
Denominator = [(√3 + √2) - √5] [(√3 + √2) + √5]
= (√3 + √2)2 - (√5)2
= (3 + 2√6 + 2) - 5
= 5 + 2√6 - 5
= 2√6
So the expression becomes: (√3 + √2 + √5) / (2√6)
Now, rationalize this denominator by multiplying by √6 / √6:
= (√6(√3 + √2 + √5)) / (2√6 × √6)
= (√18 + √12 + √30) / (2 × 6)
= (√(9 × 2) + √(4 × 3) + √30) / 12
= (3√2 + 2√3 + √30) / 12.

Q. Which of the following statements is FALSE about the number zero?

1. Zero is a rational number.
2. Zero is a natural number.
3. Zero is a whole number.
4. Zero is an integer.

Answer: B

Explanation:

Zero is a rational number because it can be written as 0/1 (p/q form where q ≠ 0). (TRUE)
2. Natural numbers are {1, 2, 3, ...}. Zero is not included in the set of natural numbers. (FALSE)
3. Whole numbers are {0, 1, 2, 3, ...}. Zero is a whole number. (TRUE)
4. Integers are {..., -2, -1, 0, 1, 2, ...}. Zero is an integer. (TRUE)

Q. Convert 0.2‾35 (where ‾35 means 35 repeats) into a fraction in its simplest form.

1. 235/999
2. 233/990
3. 235/1000
4. 233/999

Answer: B

Explanation:

Let x = 0.2‾35 = 0.2353535...
Multiply by 10 to move the non-repeating part to the left of the decimal: 10x = 2.353535... (Equation 1)
Now, multiply by 100 (since two digits are repeating) to shift the repeating block: 1000x = 235.353535... (Equation 2)
Subtract Equation 1 from Equation 2:
1000x - 10x = 235.353535... - 2.353535...
990x = 233
x = 233/990. This fraction is in simplest form as 233 is a prime number and 990 is not a multiple of 233.

Q. Simplify: ( (625)-1/2 )-1/4

1. √5
2. 1/5
3. 25
4. 1/25

Answer: A

Explanation:

Using the law of exponents (am)n = amn:
( (625)-1/2 )-1/4 = (625)(-1/2) × (-1/4)
= (625)1/8
We know that 625 = 54.
= (54)1/8
= 54 × (1/8)
= 54/8
= 51/2
= √5.

Q. Which of the following is the largest among √2, √3, 3√4, and 4√5?

√2

√3

3√4

4√5

Answer: B

Explanation:

To compare these surds, convert them to exponents with a common denominator. The indices are 2, 2, 3, and 4. The LCM of 2, 3, 4 is 12.
√2 = 21/2 = 26/12 = (26)1/12 = 641/12
√3 = 31/2 = 36/12 = (36)1/12 = 7291/12
3√4 = 41/3 = 44/12 = (44)1/12 = 2561/12
4√5 = 51/4 = 53/12 = (53)1/12 = 1251/12
Comparing the bases: 64, 729, 256, 125. The largest base is 729.
Therefore, 7291/12 (which is √3) is the largest.

Q. What is the value of ( ( (1/2)-2 )-1 )0?

1. 1
2. 0
3. 4
4. 1/4

Answer: A

Explanation:

Any non-zero number raised to the power of 0 is 1. The expression inside the outermost parentheses is a definite number (not zero).
Let's evaluate the innermost part first:
(1/2)-2 = (2/1)2 = 22 = 4.
Next, (4)-1 = 1/4.
Finally, (1/4)0 = 1.
This confirms that any non-zero base raised to the power of 0 is 1.

Q. Which of the following numbers is rational?

1. π
2. √7
3. 0.123456789101112...
4. 0.3333…

Answer: D

Explanation:

1. π is a well-known irrational number.
   2. √7 is irrational because 7 is not a perfect square.
   3. 0.123456789101112... is a non-terminating, non-recurring decimal (the digits follow a pattern of increasing integers, but it's not a repeating block), making it irrational.
   4. 0.3333... is a non-terminating recurring decimal, which can be expressed as 1/3. Therefore, it is a rational number.

Number System MCQ Preparation Tips

Follow these simple tips to score better:

• Read all options carefully before selecting an answer
• Use the elimination method to remove wrong options
• Learn the rules of rational and irrational numbers clearly
• Practice fast calculations and conversions regularly
• Solve number system MCQ class 9 online tests for better practice
• Use reliable study material based on CBSE and NCERT syllabus

Conclusion

Practicing Class 9 Maths Number System MCQs with answers is one of the best ways to understand concepts deeply. It helps students improve problem-solving skills and prepares them for school exams as well as competitive tests.