The number system is the foundation of mathematics and plays a crucial role in solving various mathematical problems. Understanding the number system is essential for students as it helps them grasp more complex mathematical concepts in the future. In this article, we will explore the fundamental concepts of the number system and provide **50 multiple-choice questions (MCQs) tailored for Class 9 students**.

### 50 multiple-choice questions (MCQs) on the number system for Class 9, along with their answers and detailed explanations:

1. MCQ: What is the smallest prime number?

a) 0

b) 1

c) 2

d) 3

Answer: c) 2

Explanation: The smallest prime number is 2, which is only divisible by 1 and itself.

2. MCQ: Which of the following is a composite number?

a) 5

b) 7

c) 11

d) 9

Answer: d) 9

Explanation: A composite number is a positive integer greater than 1 that has more

than two factors. 9 is a composite number as it can be divided by 1, 3, and 9.

3. MCQ: What is the least common multiple (LCM) of 6 and 8?

a) 12

b) 16

c) 18

d) 24

Answer: d) 24

Explanation: LCM of 6 and 8 is the smallest multiple that both numbers have in common,

which is 24.

4. MCQ: What is the greatest common divisor (GCD) of 24 and 36?

a) 6

b) 12

c) 18

d) 24

Answer: a) 6

Explanation: GCD of 24 and 36 is the largest number that divides both 24 and 36

without leaving a remainder, which is 6.

5. MCQ: Which of the following is an irrational number?

a) 4/5

b) √2

c) 1.5

d) 3.14

Answer: b) √2

Explanation: An irrational number is a number that cannot be expressed as a fraction

of two integers. √2 is irrational because it cannot be represented as a simple fraction.

6. MCQ: Which of the following is a terminating decimal?

a) 1/3

b) 1/4

c) 1/6

d) 1/7

Answer: b) 1/4

Explanation: A terminating decimal is a decimal number that ends after a

finite number of digits. 1/4 is a terminating decimal, as it can be written as 0.25.

7. MCQ: What is the decimal equivalent of the binary number 1010?

a) 8

b) 10

c) 12

d) 14

Answer: b) 10

Explanation: The binary number 1010 is equal to 1*2^3 + 0*2^2 + 1*2^1 + 0*2^0

= 8 + 0 + 2 + 0 = 10 in decimal.

8. MCQ: Express 5/8 as a percentage.

a) 40%

b) 50%

c) 62.5%

d) 80%

Answer: c) 62.5%

Explanation: To express a fraction as a percentage, multiply the fraction by 100.

5/8 * 100 = 0.625 * 100 = 62.5%.

9. MCQ: Which of the following numbers is divisible by 9?

a) 423

b) 567

c) 648

d) 751

Answer: c) 648

Explanation: A number is divisible by 9 if the sum of its digits is divisible by 9.

In this case, 6 + 4 + 8 = 18, which is divisible by 9.

10. MCQ: What is the value of 5^0?

a) 0

b) 1

c) 5

d) undefined

Answer: b) 1

Explanation: Any nonzero number raised to the power of 0 is equal to 1.

11. MCQ: Which of the following is a prime factorization of 24?

a) 2 × 12

b) 2 × 2 × 6

c) 2 × 2 × 2 × 3

d) 2 × 2 × 3 × 3

Answer: c) 2 × 2 × 2 × 3

Explanation: The prime factorization of 24 is 2 × 2 × 2 × 3, where all factors

are prime numbers.

12. MCQ: What is the sum of all natural numbers from 1 to 100?

a) 5050

b) 5000

c) 4950

d) 50500

Answer: a) 5050

Explanation: The sum of all natural numbers from 1 to n can be calculated using

the formula (n * (n + 1)) / 2. So, for n = 100, the sum is (100 * 101) / 2 = 5050.

13. MCQ: Which of the following numbers is a perfect square?

a) 25

b) 36

c) 42

d) 53

Answer: a) 25

Explanation: A perfect square is a number that can be expressed as the square

of an integer. 25 is a perfect square because it is 5^2 (5 * 5).

14. MCQ: What is the value of 0.3 recurring (0.333...) as a fraction?

a) 1/3

b) 2/3

c) 3/10

d) 1/10

Answer: a) 1/3

Explanation: The decimal 0.3 recurring can be represented as 0.333...

In fractional form, it is 1/3.

15. MCQ: What is the value of 2^4 × 2^3?

a) 32

b) 64

c) 128

d) 256

Answer: d) 256

Explanation: When multiplying numbers with the same base, you can add

their exponents. So, 2^4 × 2^3 = 2^(4+3) = 2^7 = 128.

16. MCQ: Which of the following numbers is a rational number?

a) √5

b) -2.5

c) π (pi)

d) 0.55

Answer: b) -2.5

Explanation: A rational number is a number that can be expressed as a fraction

of two integers.-2.5 is a rational number as it can be written as -5/2.

17. MCQ: What is the value of | -12 |?

a) 12

b) -12

c) 0

d) undefined

Answer

: a) 12

Explanation: The absolute value of a number is its distance from zero on the number line.

So, | -12 | = 12.

18. MCQ: Which of the following numbers is not a whole number?

a) 0

b) -3

c) 6

d) 9

Answer: b) -3

Explanation: Whole numbers include all positive integers and zero. -3 is an integer

but not a whole number as it is negative.

19. MCQ: What is the reciprocal of 2/5?

a) 2/5

b) 5/2

c) 1/2

d) 5/1

Answer: b) 5/2

Explanation: The reciprocal of a fraction is obtained by interchanging its numerator and

denominator. So,the reciprocal of 2/5 is 5/2.

20. MCQ: Which of the following numbers is a perfect cube?

a) 27

b) 32

c) 49

d) 64

Answer: a) 27

Explanation: A perfect cube is a number that can be expressed as the cube of an integer.

27 is a perfect cube because it is 3^3 (3 * 3 * 3).

21. MCQ: What is the smallest number that can be added to 300 to make it divisible by 7?

a) 1

b) 2

c) 3

d) 4

Answer: b) 2

Explanation: To make 300 divisible by 7, we need to find the remainder when 300

is divided by 7. 300 ÷ 7 = 42 with a remainder of 6. So, we need to add 7 - 6 = 1 to 300

to make it divisible by 7.

22. MCQ: What is the value of 0.09 as a percentage?

a) 0.9%

b) 9%

c) 90%

d) 900%

Answer: c) 90%

Explanation: To express a decimal as a percentage, multiply the decimal

by 100. 0.09 * 100 = 9%.

23. MCQ: Which of the following numbers is a prime number?

a) 15

b) 19

c) 28

d) 30

Answer: b) 19

Explanation: A prime number is a number greater than 1 with no positive divisors other

than 1 and itself. 19 is a prime number as it only has two factors: 1 and 19.

24. MCQ: What is the value of 1/5 ÷ 0.2?

a) 0.25

b) 0.5

c) 1

d) 5

Answer: d) 5

Explanation: To divide by a decimal, multiply by its reciprocal. So, 1/5 ÷ 0.2 is

the same as 1/5 * 5 = 1.

25. MCQ: What is the value of 3! (3 factorial)?

a) 3

b) 6

c) 9

d) 12

Answer: b) 6

Explanation: Factorial of a number is the product of all positive integers up to

that number. 3! = 3 * 2 * 1 = 6.

26. MCQ: Which of the following numbers is a multiple of 4?

a) 25

b) 28

c) 33

d) 40

Answer: b) 28

Explanation: A multiple of a number is obtained by multiplying that number

by any integer.28 is a multiple of 4 as it is 4 * 7.

27. MCQ: What is the value of 9^2 - 8^2?

a) 1

b) 17

c) 41

d) 73

Answer: b) 17

Explanation: To find the difference between two squares, use the formula (a - b)(a + b).

So, 9^2 - 8^2 = (9 - 8)(9 + 8) = 1 * 17 = 17.

28. MCQ: Express 7/20 as a decimal.

a) 0.35

b) 0.7

c) 0.75

d) 0.14

Answer: a) 0.35Explanation: Divide the numerator (7) by the denominator (20) to convert the fraction to a

decimal. 7 ÷ 20 = 0.35.

29. MCQ: Which of the following numbers is not a perfect square?

a) 81

b) 100

c) 144

d) 256

Answer: d) 256

Explanation: A perfect square is a number that can be expressed as the square of an integer.

256 is a perfect square because it is 16^2. All the other options are perfect squares as well.

30. MCQ: What is the value of 3^5?

a) 9

b) 15

c) 81

d) 243

Answer: d) 243

Explanation: 3^5 means 3 raised to the power of 5, which is 3 * 3 * 3 * 3 * 3 = 243.

31. MCQ: What is the value of (4 + 5) × (6 - 2)?

a) 14

b) 18

c) 20

d) 24

Answer: c) 20

Explanation: Perform the operations in parentheses first: (4 + 5) = 9 and (6 - 2) = 4.

Then, multiply the results: 9 × 4 = 36.

32. MCQ: What is the product of the first three prime numbers?

a) 6

b) 15

c) 30

d) 60

Answer: c) 30

Explanation: The first three prime numbers are 2, 3, and 5. The product of these

numbers is 2 * 3 * 5 = 30.

33. MCQ: Which of the following numbers is a perfect cube?

a) 64

b) 81

c) 100

d) 125

Answer: d) 125

Explanation: A perfect cube is a number that can be expressed as the cube of an integer.

125 is a perfect cube because it is 5^3 (5 * 5 * 5).

34. MCQ: What is the value of 2^0 + 2^1 + 2^2 + 2^3 + 2^

4?

a) 8

b) 16

c) 24

d) 32

Answer: b) 16

Explanation: The expression represents the sum of powers of 2 from 2^0 to 2^4.

The sum is 1 + 2 + 4 + 8 + 16 = 31.

35. MCQ: What is the smallest prime factor of 63?

a) 3

b) 7

c) 9

d) 12

Answer: a) 3

Explanation: The prime factorization of 63 is 3 * 3 * 7. The smallest prime factor is 3.

36. MCQ: What is the value of √16 + √25?

a) 6

b) 7

c) 8

d) 9

Answer: b) 7

Explanation: √16 = 4 and √25 = 5. So, √16 + √25 = 4 + 5 = 9.

37. MCQ: Which of the following is a non-terminating repeating decimal?

a) 0.125

b) 0.4

c) 0.333...

d) 0.6

Answer: c) 0.333...

Explanation: A non-terminating repeating decimal has a recurring pattern of digits

after the decimal point. 0.333... is a non-terminating repeating decimal.

38. MCQ: What is the value of 10% of 400?

a) 4

b) 10

c) 40

d) 100

Answer: c) 40

Explanation: To find 10% of a number, multiply the number by 0.1. So, 10% of 400 is 0.1 * 400 = 40.

39. MCQ: What is the smallest composite number?

a) 0

b) 1

c) 2

d) 4

Answer: d) 4

Explanation: A composite number is a positive integer greater than 1 that has more

than two factors. The smallest composite number is 4.

40. MCQ: What is the value of 0.2 as a fraction in simplest form?

a) 1/2

b) 1/4

c) 2/10

d) 1/5

Answer: d) 1/5

Explanation: 0.2 can be written as 2/10. To simplify the fraction, divide both

the numerator and denominator by their greatest common divisor, which is 2.

So, 2/10 simplifies to 1/5.

41. MCQ: What is the sum of the first five prime numbers?

a) 15

b) 19

c) 22

d) 28

Answer: b) 19

Explanation: The first five prime numbers are 2, 3, 5, 7, and 11.

The sum of these numbers is 2 + 3 + 5 + 7 + 11 = 28.

42. MCQ: What is the value of 5^3 ÷ 5^2?

a) 5

b) 10

c) 15

d) 25

Answer: a) 5

Explanation: When dividing numbers with the same base, subtract the exponents.

So, 5^3 ÷ 5^2 = 5^(3-2) = 5^1 = 5.

43. MCQ: What is the value of 1/3 ÷ 0.1?

a) 0.03

b) 0.1

c) 0.3

d) 3

Answer: d) 3

Explanation: To divide by a decimal, multiply by its reciprocal. So, 1/3 ÷ 0.1 is

the same as 1/3 * 10 = 10/3 = 3.

44. MCQ: Which of the following is a rational number?

a) √10

b) √9

c) √5

d) √16

Answer: b) √9

Explanation: A rational number is a number that can be expressed as a fraction of

two integers. √9 is a rational number as it is equal to 3, which can be written as 3/1.

45. MCQ: What is the value of 12% of 250?

a) 25

b) 30

c) 50

d) 75

Answer: b) 30

Explanation: To find 12% of a number, multiply the number by 0.12.

So, 12% of 250 is 0.12 * 250 = 30.

46. MCQ: What is the value of 1/6 as a recurring decimal?

a) 0.15

b) 0.2

c) 0.166...

d) 0.17

Answer: c) 0.166...

Explanation: The fraction 1/6 can be expressed as a recurring decimal as 0.166...

where 6 repeats infinitely.

47. MCQ: What is the sum of all even numbers between 20 and 40?

a) 400

b) 420

c) 440

d) 460

Answer: b) 420

Explanation: The sum of an arithmetic sequence can be calculated using

the formula (n/2) * (first term + last term). In this case,

the first term is 20, the last term is 40, and the number

of terms (n) is (40 - 20)/2 + 1 = 11. So, the sum is (11/2) * (20 + 40) = 11 * 30 = 330.

48. MCQ: Which of the following numbers is a multiple of 9?

a) 63

b) 72

c) 81

d) 90

Answer: b) 72

Explanation: A number is divisible by 9 if the sum of its digits is divisible by 9.

In this case, 7 + 2 = 9, which is divisible by 9.

49. MCQ: What is the value of 0.5 × 0.5 × 0.5?

a) 0.125

b) 0.25

c) 0.375

d) 0.5

Answer: a) 0.125

Explanation: To find the product of multiple decimals, multiply the numbers

together. 0.5 × 0.5 × 0.5 = 0.125.

50. MCQ: What is the largest three-digit number?

a) 999

b) 1000

c) 1001

d) 1002

Answer: a) 999

Explanation: The largest three-digit number is 999, as it is the highest number

formed by using three digits.

The number system is the bedrock of mathematics, and a solid understanding of its concepts is essential for students. By mastering the number system, students can tackle more complex mathematical challenges and develop critical problem-solving abilities.

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