What is a CBSE Class 8 Exponents Case Study with Solutions?

A CBSE Class 8 Exponents Case Study with Solutions helps students understand laws of exponents, powers, and standard form. It includes solved examples, step-by-step answers, and real-life applications of exponents based on the CBSE Class 8 Mathematics syllabus.

How can I download CBSE Class 8 Exponents Case Study PDFs?

You can download free CBSE Class 8 Exponents Case Study PDFs with complete solutions from educational websites offering Class 8 Maths study materials and chapter-wise practice sets.

What are the important topics covered in Class 8 Exponents and Powers?

Important topics in Class 8 Exponents and Powers include laws of exponents, powers of integers, standard form, and numerical problem-solving. These concepts form the base for algebra and scientific notation.

How do video tutorials help in solving CBSE Class 8 Exponents Case Studies?

Video tutorials explain each law of exponents with examples, making it easier to solve CBSE Class 8 Exponents Case Studies. They provide clear visual steps and interactive explanations for better understanding.

Why should students practice CBSE Class 8 Exponents Case Study Questions?

Practicing CBSE Class 8 Exponents Case Study Questions helps students apply theoretical knowledge to practical problems, enhance logical reasoning, and improve accuracy in exams.

CBSE Class 8 Exponents Case Study with Solutions

During a science exhibition, students created a model of a rocket launch simulation. To understand real-life space measurements, they studied how scientists use exponents and powers in expressing large and small quantities. The average distance between Earth and Moon is approximately \(3.84 \times 10^5\) km, while the speed of light is \(3 \times 10^8\) m/s. For their simulation, they designed a miniature spacecraft that could travel at \(2 \times 10^3\) m/s. The team wanted to calculate how long it would theoretically take their spacecraft to reach the Moon if it could travel directly. They also learned to express very small values like mass of particles and large distances using scientific notation to make comparisons easier. This project helped them appreciate how exponents simplify real-world scientific data representation.

1. Convert the speed of the spacecraft \(2 \times 10^3\) m/s into km/s.

(A) \(2 \times 10^3\) km/s

(B) \(2 \times 10^0\) km/s

(D) \(2 \times 10^{-2}\) km/s

Solution:

\(1 \text{ km} = 10^3 \text{ m}\). Therefore, \(2 \times 10^3 \text{ m/s} = 2 \times 10^3 \times 10^{-3} = 2 \times 10^{0} = 2 \text{ km/s.}\) Hence, in km/s, exponent form is \(2 \times 10^{0}\).

2. If the Moon is \(3.84 \times 10^5\) km away, how many seconds will the spacecraft take to reach it at a speed of \(2 \text{ km/s}\)?

(A) \(1.92 \times 10^5\) s

(B) \(1.92 \times 10^6\) s

(D) \(7.68 \times 10^4\) s

Solution:

Time \(= \dfrac{\text{distance}}{\text{speed}} = \dfrac{3.84 \times 10^5}{2} = 1.92 \times 10^5\) s.

3. Express \(0.00012\) in standard form.

(A) \(1.2 \times 10^{-4}\)

(B) \(1.2 \times 10^{-5}\)

(D) \(1.2 \times 10^{4}\)

Solution:

\(0.00012 = 1.2 \times 10^{-4}\) since the decimal is moved 4 places to the right.

4. The mass of a dust particle is \(3 \times 10^{-7}\) kg and there are \(2 \times 10^3\) such particles. What is the total mass?

(A) \(6 \times 10^{-4}\) kg

(B) \(6 \times 10^{-3}\) kg

(D) \(5 \times 10^{-3}\) kg

Solution:

Total mass \(= 3 \times 10^{-7} \times 2 \times 10^3 = 6 \times 10^{-7+3} = 6 \times 10^{-4}\) kg.

5. Which of the following represents a larger number?

(A) \(4 \times 10^6\)

(B) \(3.5 \times 10^7\)

(D) \(9 \times 10^4\)

Solution:

Comparing powers of 10, the greatest exponent corresponds to the largest number. Hence, \(10^7\) is greater than \(10^6, 10^5, 10^4.\)

CBSE Class 8 Exponents Case Study with Solutions

CBSE Class 8 Exponents Case Study with Solutions

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Case Study 2: CBSE Class 8 Exponents Case Study with Solutions

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