How can students prepare for Class 8 Exponents and Standard Form case studies?

Students can prepare for Class 8 Exponents and Standard Form case studies by solving NCERT-based worksheets, watching video tutorials, and downloading solved PDFs for practice and revision.

What are the main laws of exponents in Class 8 Mathematics?

The main laws of exponents include the product law, quotient law, and power of a power rule. These concepts are essential for solving Class 8 Exponents and Standard Form case study questions accurately.

Why is learning Standard Form important in Class 8 Maths?

Learning Standard Form in Class 8 Maths helps students represent very large or small numbers efficiently. It simplifies complex calculations and is widely used in scientific and real-life applications.

How do video tutorials help in solving Exponents and Standard Form questions?

Video tutorials provide step-by-step explanations of Exponents and Standard Form concepts, helping Class 8 students visualize problems and understand how to apply exponent laws effectively.

Exponents and Standard Form Case Study Questions Class 8

Q: What are Exponents and Standard Form Case Study Questions for Class 8?

Exponents and Standard Form Case Study Questions for Class 8 help students understand the laws of exponents and scientific notation. These questions involve converting numbers into standard form and applying exponent rules as per the CBSE syllabus.

A group of geography students were researching how population changes over time can be expressed using powers and exponents. They studied a city that had a population of \(2 \times 10^5\) people in the year 2000. Every 10 years, the population increased by a factor of \(2 \times 10^0\) (i.e., it doubled every decade). The students wanted to predict the population for the years 2010, 2020, and 2030. They also compared it with another town whose growth rate was slower — it increased only by a factor of \(5 \times 10^{-1}\) per decade. By applying the laws of exponents and converting their results into standard form, they could easily analyze long-term growth trends and make population projections.

1. What will be the population of the city in 2010?

(A) \(4 \times 10^5\)

(B) \(2 \times 10^5\)

(D) \(3 \times 10^5\)

Solution:

Each decade population doubles, so \(2 \times 10^5 \times 2 = 4 \times 10^5\).

2. What will be the population of the city in 2020?

(A) \(8 \times 10^5\)

(B) \(1.6 \times 10^6\)

(D) \(6 \times 10^5\)

Solution:

In 20 years, it doubles twice. Population \(= 2 \times 10^5 \times 2^2 = 2 \times 4 \times 10^5 = 8 \times 10^5\).

3. The other town grows by a factor of \(5 \times 10^{-1}\) per decade. If its population in 2000 was \(2 \times 10^5\), what is its population in 2010?

(A) \(1 \times 10^5\)

(B) \(1.5 \times 10^5\)

(D) \(2.5 \times 10^5\)

Solution:

\(2 \times 10^5 \times 5 \times 10^{-1} = (2 \times 5) \times 10^{5-1} = 10 \times 10^4 = 1 \times 10^5.\)

4. By 2030, what will be the population of the first city if it continues to double every 10 years?

(A) \(1.6 \times 10^6\)

(B) \(1.2 \times 10^6\)

(D) \(2.4 \times 10^6\)

Solution:

\(2 \times 10^5 \times 2^3 = 2 \times 8 \times 10^5 = 1.6 \times 10^6.\)

5. If the population of the smaller town decreases to half every decade, express its 2030 population as a power of 10 starting from \(2 \times 10^5\).

(A) \(2 \times 10^4\)

(B) \(2.5 \times 10^4\)

(D) \(2 \times 10^3\)

Solution:

It halves thrice (2000–2010–2020–2030): \(2 \times 10^5 \times (10^{-1})^3 = 2 \times 10^{5-3} = 2 \times 10^2 = 2 \times 10^4.\)

Exponents and Standard Form Case Study Questions Class 8

Exponents and Standard Form Case Study Questions Class 8

Key Concepts of Exponents and Standard Form

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Case Study 3: Exponents and Standard Form Case Study Questions Class 8

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