Class 8 Maths Chapter 2 Notes : Power Play Notes Ganita Prakash (New Book NCERT)
Are you looking for Class 8 Maths Chapter 2 Notes? In this special article, we will explain all the important formulas, patterns, and tricks of Power Play in detail according to the Ganita Prakash (New NCERT) syllabus. These Class 8 Maths Chapter 2 notes will help strengthen your foundation not only for school exams but also for competitive exams.
Class 8 Maths Chapter 2: Power Play – The Easiest Notes
Have you ever thought about how powerful a small number can be in mathematics? In this chapter “Power Play,” we will understand the magic of exponents. Imagine if you could fold a piece of paper only \( 46 \) times, its thickness would increase so much that it would reach the Moon. All this happens because of the increasing power of exponents.
This post, in the form of Class 8 Maths Chapter 2 Notes, will help you understand the laws of exponents, writing large numbers in simplified form, and the scientific method.
Power Play Class 8 Maths Notes
What is an Exponent? (Understanding Exponents)
When the same number is multiplied repeatedly, the method of writing it in short form is called an exponent.
Definition: If \( a \) is multiplied \( n \) times, it is written as \( a^n \).
Example: \( 5 \times 5 \times 5 = 5^3 \).
Here, \( 5 \) is called the ‘base’ and \( 3 \) is called the ‘exponent’.
The Paper Folding Experiment
According to the chapter, every time a paper is folded, the number of layers doubles:
\( 0 \) folds = \( 2^0 = 1 \) layer
\( 1 \) fold = \( 2^1 = 2 \) layers
\( 2 \) folds = \( 2^2 = 4 \) layers
\( n \) folds = \( 2^n \) layers
Important Formula: If the thickness of the paper is \( 0.001 \text{ cm} \), then after \( n \) folds the thickness will be \( 0.001 \times 2^n \text{ cm} \).
Laws of Exponents
To make calculations easier, follow these rules:
Law of multiplication: \( a^m \times a^n = a^{m+n} \)
Law of division: \( a^m \div a^n = a^{m-n} \)
Power of a power: \( (a^m)^n = a^{m \times n} \)
Power of zero: \( a^0 = 1 \) (where \( a \neq 0 \))
Same exponents (multiplication): \( a^n \times b^n = (a \times b)^n \)
Scientific Notation or Standard Form
To read and write very large numbers, we use scientific notation.
Standard form: \( x \times 10^y \)
Where \( 1 \le x < 10 \) and \( y \) is an integer.
Example: The standard form of \( 30,81,00,000 \) is \( 3.081 \times 10^8 \).
Comparing Large Numbers
While comparing numbers, always focus on their powers.
Example: Which is greater, \( 10^{13} \) or \( (10^6)^2 \)?
Since \( (10^6)^2 = 10^{12} \) and \( 13 > 12 \), therefore \( 10^{13} \) is greater.
Class 8 Maths Chapter 2 Conclusion
In this chapter, we learned how the laws of exponents make large calculations easy. Remember that when the exponent of any number is zero, its value is \( 1 \), and scientific notation is the most accurate way to measure very large distances. This “Power Play” chapter forms a foundation for your future Algebra.
FAQs on Power Play Class 8 Maths Notes
Q 1. Why is the value of \( a^0 \) always \( 1 \)?
Ans. According to the law of division \( a^m \div a^m = a^{m-m} = a^0 \). When we divide a number by itself, the result is \( 1 \). That is why \( a^0 = 1 \).
Q 2. What should be the value of \( x \) in scientific notation?
Ans. In scientific notation \( x \times 10^y \), the value of \( x \) should always be greater than or equal to \( 1 \) and less than \( 10 \), that is \( (1 \le x < 10) \).
Q 3. What is the value of \( 2^{10} \)?
Ans. The value of \( 2^{10} \) is \( 1024 \).
Q 4. What is ‘Googol’?
Ans. In mathematics, the number \( 10^{100} \) is called a ‘Googol’, which is a very large number.
Q 5. How do we multiply when the bases are different but the exponents are the same?
Ans. Use the rule \( a^n \times b^n = (ab)^n \). For example, \( 2^3 \times 5^3 = (2 \times 5)^3 = 10^3 = 1000 \).
Q 6. How do we write \( 1,50,000 \) in standard form?
Ans. It is written in standard form as \( 1.5 \times 10^5 \).
Q 7. Is it really possible to fold a paper 46 times?
Ans. Practically, it is very difficult to fold an ordinary paper more than 7 to 8 times, but mathematically, folding it 46 times would make its thickness reach the Moon.
Q 8. Using the laws of exponents, what is the value of \( 5^7 \div 5^4 \)?
Ans. According to the rule \( a^m \div a^n = a^{m-n} \): \( 5^{7-4} = 5^3 = 125 \).
Q 9. What is the result when the exponent of a negative base is even?
Ans. If the exponent of a negative base is even, the result is always positive. For example, \( (-2)^2 = 4 \).
Q 10. What is the use of exponents in daily life?
Ans. Exponents are used in computer memory units (KB, MB, GB), measuring bacterial growth, and calculating astronomical distances.
Stay tuned for practice and keep learning such interesting concepts of mathematics by reading the notes of the next chapter!
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