Number System- Case Based Type Questions

# Class 8 Maths Chapter 1 Case Based Questions - Number System

Q1: Democracy has given people a powerful right- that is to VOTE. In India, every citizen over 18 years of age has the right to vote. Instead of enjoying it as a holiday, one must vote if he/she truly wants to contribute to the nation-building process and bring about a change.
A survey was done in a small area in which voters were men andvoters were women.
Which mathematical concept is used here?
(a) Number system
(b) Circle
(c) Area
(d) Statistics

Sol:

Number system: A numeral system (or system of numeration) is a writing system for expressing numbers that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The number the numeral represents is called its value.

Q2: Democracy has given people a powerful right- that is to VOTE. In India, every citizen over 18 years of age has the right to vote. Instead of enjoying it as a holiday, one must vote if he/she truly wants to contribute to the nation-building process and bring about a change.
A survey was done in a small area in which voters were men andvoters were women.

(a)
(b)
(c)
(d)

Sol:

Q3: Democracy has given people a powerful right- that is to VOTE. In India, every citizen over 18 years of age has the right to vote. Instead of enjoying it as a holiday, one must vote if he/she truly wants to contribute to the nation-building process and bring about a change.
A survey was done in a small area in which voters were men andvoters were women.
Find x, if number of men is equal to number of women.
(a) 6
(b) 5
(c) 8
(d) 9

Sol:

⇒ 9 + 2x – 5 =
⇒ 4 + 2x =
Squaring both sides,
(4 + 2x)2 =
⇒ 16 + 4x2 + 16x = 18x + 4x2

⇒ 16 = 2x

⇒ x = 8

Q4:Democracy has given people a powerful right- that is to VOTE. In India, every citizen over 18 years of age has the right to vote. Instead of enjoying it as a holiday, one must vote if he/she truly wants to contribute to the nation-building process and bring about a change.
A survey was done in a small area in which voters were men andvoters were women.
Q. ap . aq =
(a) ap + q
(b) ap – q
(c) apq
(d) (pq)a

Sol:

ap + q
ap . aq = ap + q

Q5:Democracy has given people a powerful right- that is to VOTE. In India, every citizen over 18 years of age has the right to vote. Instead of enjoying it as a holiday, one must vote if he/she truly wants to contribute to the nation-building process and bring about a change.
A survey was done in a small area in which voters were men andvoters were women.
Q. If r is rational and s is irrational, then which statement is false?
(a) r + s is irrational number.
(b) r – s is rational number.
(c) rs is irrational number.
(d) r/s is irrational number.

Sol:

r – s is rational number.

Reason : This statement is false. The difference between a rational number (r) and an irrational number (s) can be either rational or irrational. There is no general rule that says the difference of a rational and an irrational number must be rational. Counterexamples can easily be constructed to show that the difference could be either rational or irrational.

Q6: In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities.
What is the value of 5/7 ?
(a)
(b) 1.4
(c) 1.414
(d) 1.7142

Sol:

5 ÷ 7 =

Q7: In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities.
How many rational numbers are there between 5 and 7.

(a) 0
(b) 1
(c) 2
(d) infinite

Sol:

There are an infinite amount of irrational numbers between 5 and 7.

Q8:In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities.
What fraction of the students participated in the campaign.
(a) 2/7
(b) 5/7
(c) 4/7
(d) 7/7

Sol:

Number of students participated in campaign = 5

Number of total students = 7

Therefore, fraction of the students participated in the campaign. = 5/7

Q9:In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities.
What kind of decimal expansion it has.
(a) Terminating
(b) non terminating
(c) terminating repeating
(d) non terminating repeating

Sol:

A non-terminating, non-repeating decimal is a decimal number that continues endlessly, with no group of digits repeating endlessly. Decimals of this type cannot be represented as fractions, and as a result are irrational numbers. Non-terminating, non-repeating decimals can be easily created by using a pattern.

Q10:In a school 5 out of every 7 children participated in ‘Save wild life’ campaign organised by the school authorities.
Every rational number is a _______ number.
(a)
Prime
(b)
Composite
(c)
real
(d)
even

Sol:

Every rational number is a real number.
It can be defined as any number that can be expressed in the p/q form where q ≠ 0. We can also say that any fraction falls under the class of rational numbers, where the denominator and numerator are integers and the denominator is not equal to zero.

The document Class 8 Maths Chapter 1 Case Based Questions - Number System is a part of the Class 8 Course Advance Learner Course: Mathematics (Maths) Class 8.
All you need of Class 8 at this link: Class 8

## Advance Learner Course: Mathematics (Maths) Class 8

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## FAQs on Class 8 Maths Chapter 1 Case Based Questions - Number System

 1. What is the decimal number system?
Ans. The decimal number system is a base-10 number system that uses the digits 0-9 to represent numbers. It is the most commonly used number system in everyday life and in mathematics. Each digit in a decimal number has a place value, and the value of a number is determined by the sum of the products of each digit and its corresponding place value.
 2. What is the binary number system?
Ans. The binary number system is a base-2 number system that uses only two digits, 0 and 1, to represent numbers. It is commonly used in computer science and digital electronics. In the binary system, each digit has a place value that is a power of 2, and the value of a number is determined by the sum of the products of each digit and its corresponding place value.
 3. How do you convert a decimal number to a binary number?
Ans. To convert a decimal number to a binary number, you can use the process of division by 2. Start by dividing the decimal number by 2 and noting the remainder. Then, divide the quotient by 2 and note the remainder again. Continue this process until the quotient becomes 0. The binary number is obtained by writing the remainders in reverse order.
 4. How do you convert a binary number to a decimal number?
Ans. To convert a binary number to a decimal number, you can use the process of multiplying each digit by its corresponding power of 2 and summing the results. Start from the rightmost digit and multiply it by 2 raised to the power of 0. Then, move to the left and multiply the next digit by 2 raised to the power of 1, and so on. Finally, sum all the products to obtain the decimal equivalent.
 5. What is the hexadecimal number system?
Ans. The hexadecimal number system is a base-16 number system that uses the digits 0-9 and the letters A-F to represent numbers. It is commonly used in computer science and digital electronics due to its compact representation of binary numbers. In the hexadecimal system, each digit has a place value that is a power of 16, and the value of a number is determined by the sum of the products of each digit and its corresponding place value.

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