CBSE Class 8 Mathematics Chapter 10 ‘Exponents and Powers’ Notes

Introduction:

Welcome to Online Tutorial Classes! We are excited to present a valuable resource for CBSE students studying Class 8 Mathematics. In this post, we will delve into the CBSE class 8 Mathematics Chapter 10 ‘Exponents and Powers’ from the CBSE curriculum and provide you with a comprehensive notes and worksheets to help you master this important topic.

CBSE Class 8 Mathematics Chapter 10, ‘Exponents and Powers’, introduces students to the concept of exponents and powers, including negative exponents, and explains how to express large and small numbers in standard form using exponents. The chapter also covers the laws of exponents.

NCERT Maths book:

Click here to access and download the NCERT class 8 Mathematics book.

CBSE class 8 Mathematics Chapter 10 ‘Exponents and Powers’ Overview

CBSE Class 8 Mathematics Chapter 10, ‘Exponents and Powers’, introduces the fundamental concepts of exponents and powers. The chapter explains how these mathematical tools can be used to express large and small numbers in a more convenient form. It also covers the laws of exponents and provides numerous examples and practice problems to help students understand and apply these concepts. The chapter is designed to help students build a strong foundation in the concept of exponents and powers, preparing them for more advanced mathematical studies.

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CBSE class 8 Maths Chapter 10 ‘Exponents and Powers’ Notes

Introduction to Exponents and Powers

The power of a number indicates the number of times it must be multiplied. It is written in the form

Here ‘a’ is called the base and ‘b’ is called the exponent. For example: Consider

Here the exponent ‘3’ indicates that base ‘9’ needs to be multiplied three times to get our equivalent answer which is 729.

Powers with Negative Exponents

A negative exponent in power for any non-integer is basically a reciprocal of the power. In simple terms, for a non-zero integer a with an exponent -b,

Expanding a Rational Number Using Powers

A given rational number can be expressed in expanded form with the help of exponents. For example, 1425.36 can be written as

Laws of Exponents

• Exponents with like Bases: Given a non-zero integer a,

where m and n are integers. and

where m and n are integers.

Power of a Power: Given a non-zero integer a,

where m and n are integers.

Any number to the power 0 is always 1: Given a non-zero integer a,

Exponents with Unlike Bases and Same Exponent: Given two non-zero integers a and b,

where m is an integer.

Use of Exponents to Express Small Numbers in Standard Form

Very large numbers or very small numbers can be represented in the standard form with the help of exponents. For example, if it is a very large number like 150,000,000,000, then we need to move the decimal place towards the left.

Observe the following facts.

1. The distance from the Earth to the Sun is 149,600,000,000 m.
2. The speed of light is 300,000,000 m/sec.
3. Thickness of Class VII Mathematics book is 20 mm.
4. The average diameter of a Red Blood Cell is 0.000007 mm.
5. The thickness of human hair is in the range of 0.005 cm to 0.01 cm.
6. The distance of moon from the Earth is 384, 467, 000 m (approx).
7. The size of a plant cell is 0.00001275 m.
8. Average radius of the Sun is 695000 km.
9. Mass of propellant in a space shuttle solid rocket booster is 503600 kg.
10. Thickness of a piece of paper is 0.0016 cm.
11. Diameter of a wire on a computer chip is 0.000003 m.
12. The height of Mount Everest is 8848 m.

Observe that there are few numbers which we can read like 2 cm, 8848 m, 6,95,000 km. There are some large numbers like 150,000,000,000 m which can be written as:

and some very small numbers like 0.000007 m.

Comparing very large and small numbers

In order to compare two large or small quantities, we convert them to their standard exponential form and divide them.

Comparing Diameters of the Sun and the Earth:

The diameter of the Sun is

and the diameter of the Earth is

Therefore,

which is approximately 109.

the diameter of the Sun is about 109 times the diameter of the Earth.

So the diameter of the Sun is 109 times that of the Earth!

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Accessing All Chapters of CBSE Clas 8 Mathematics:

If you’d like to explore more chapters from the CBSE Class 8 Mathematics book, you can easily access them on our website. We’ve organized all the chapters in one convenient location, making it effortless for you to navigate and study at your own pace. Simply click on the link below to access the page containing links to all the chapters of the book.

CBSE class 8 Mathematics Notes

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