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NCERT Solutions for Class 8 Maths Chapter 10 - Exponents and Powers Exercise 10.2

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NCERT Solutions for Maths Class 8 Chapter 10 Exercise 10.2 - FREE PDF Download

NCERT Solutions for Maths Exercise 10.2 Class 8 Chapter 10 - Exponents and Powers by Vedantu help students understand the basics of exponents and powers. This exercise focuses on important rules like multiplying and dividing powers, and raising a power to another power. These are key ideas for solving NCERT Solutions for Maths Class 8 problems easily.

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Table of Content
1. NCERT Solutions for Maths Class 8 Chapter 10 Exercise 10.2 - FREE PDF Download
2. Glance on NCERT Solutions Maths Chapter 10 Exercise 10.2 Class 8 | Vedantu
3. Access NCERT Solutions for Maths Class 8 Chapter 10 - Exponents and Powers
4. Class 8 Maths Chapter 10: Exercises Breakdown
5. CBSE Class 8 Maths Chapter 10 Other Study Materials
6. Chapter-Specific NCERT Solutions for Class 8 Maths
7. Important Related Links for CBSE Class 8 Maths
FAQs


By working through these problems in this exercise, students can get better at using exponents and powers. The solutions are made simple so that students can easily understand and use them. Vedantu's CBSE Class 8 Maths Syllabus make sure students can solve problems with confidence and build a strong maths foundation.


Glance on NCERT Solutions Maths Chapter 10 Exercise 10.2 Class 8 | Vedantu

  • Class 8 Maths Chapter 10 Exercise 10.2 solutions explains how to use exponents and powers in various situations.

  • It focuses on comparing very large and very small numbers using exponents to make understanding their sizes easier. 

  • It also covers the use of exponents to express small numbers, which simplifies writing and comprehending very small values. 

  • Writing numbers in standard form helps in making calculations more manageable.

  • The problems in this exercise cover these concepts, providing practice to strengthen understanding. 

  • Vedantu's expert solutions ensure clear and accurate problem-solving.

  • This article contains exercise notes, important questions, exemplar solutions, exercises and video links for Exercise 10.2 - Exponents and Powers, which you can download as PDFs.

  • There are 4 fully solved questions in Chapter 10 Exercise 10.2 Exponents and Powers.

Access NCERT Solutions for Maths Class 8 Chapter 10 - Exponents and Powers

EXERCISE 10.2

1. Express the following numbers in standard form.

(i) \[0.0000000000085\]

Ans: A number is in the standard form, if it is written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number. 

As we move the decimal from left to right, then the power of 10 increases with a negative sign.

Therefore,

\[0.0000000000085\] can be written as,

\[{\text{0}}{\text{.0000000000085}} = 8.5 \times {10^{ - 12}}\]

(ii) \[0.00000000000942\]

Ans: A number is in the standard form, if it is written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number. 

As we move the decimal from left to right, then the power of 10 increases with a negative sign.

Therefore,

\[0.00000000000942\] can be written as,

\[0.00000000000942 = 9.42 \times {10^{ - 12}}\]

(iii) \[6020000000000000\]

Ans: A number is in the standard form, if it is written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number.  

As we move the decimal from right to left, then the power of 10 increases with a positive sign.

Therefore,

\[6020000000000000\] can be written as,

\[{\text{6020000000000000}} = 6.02 \times {10^{15}}\]


(iv) \[0.00000000837\]

Ans: A number is in the standard form, if it is written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number.

As we move the decimal from left to right, then the power of 10 increases with a negative sign.

Therefore,

\[0.00000000837\] can be written as,

\[0.00000000837 = 8.37 \times {10^{ - 9}}\]

(v) \[31860000000\]

Ans: A number is in the standard form, if it is written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number.

As we move the decimal from right to left, then the power of 10 increases with a positive sign.

Therefore,

\[31860000000\] can be written as,

\[31860000000 = 3.186 \times {10^{10}}\]

2. Express the following numbers in usual form.

(i) \[{\text{3}}{\text{.02}} \times {\text{1}}{{\text{0}}^{ - 6}}\]

Ans: A number is in the usual form, if it is not written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number and is simplified and written without the help of ${10^b}$.

In expanded form this can be written as,

\[{\text{3}}{\text{.02}} \times {\text{1}}{{\text{0}}^{ - 6}} = 0.00000302\]

(ii) \[4.5 \times {10^4}\]

Ans: A number is in the usual form, if it is not written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number and is simplified and written without the help of ${10^b}$.

In expanded form this can be written as,

\[4.5 \times {10^4} = 45000\]

(iii) \[3 \times {10^{ - 8}}\]

Ans: A number is in the usual form, if it is not written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number and is simplified and written without the help of ${10^b}$.

In expanded form this can be written as,

\[3 \times {10^{ - 8}} = 0.00000003\]

(iv) \[1.0001 \times {10^9}\]

Ans: A number is in the usual form, if it is not written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number and is simplified and written without the help of ${10^b}$.

In expanded form this can be written as,

\[1.0001 \times {10^9} = 1000100000\]

(v) \[5.8 \times {10^{12}}\]

Ans: A number is in the usual form, if it is not written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number and is simplified and written without the help of ${10^b}$.

In expanded form this can be written as,

\[5.8 \times {10^{12}} = 5800000000000\]

(vi) \[3.61492 \times {10^6}\]

Ans: A number is in the usual form, if it is not written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number and is simplified and written without the help of ${10^b}$.

In expanded form this can be written as,

\[3.61492 \times {10^6} = 3614920\]

3. Express the number appearing in the following statements in standard form.

(i) 1 micron is equal to \[\dfrac{1}{{1000000}}m\].

Ans: A number is in the standard form, if it is written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number. 

\[\dfrac{1}{{1000000}}m = 0.000001m\]

As we move the decimal from left to right then the power of 10 increases with a negative sign.

Therefore,

\[0.000001m\] can be written as,

\[0.000001m = 1 \times {10^{ - 6}}\].

(ii) Charge of an electron is \[0.000,000,000,000,000,000,16{\text{ }}coulomb\].

Ans: A number is in the standard form, if it is written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number. 

Charge on an electron is \[0.000,000,000,000,000,000,16{\text{ }}coulomb\] .

As we move the decimal from left to right then the power of 10 increases with a negative sign.

Therefore,

Charge on electron can be written as,

\[0.000,000,000,000,000,000,16{\text{ }}coulomb = 1.6 \times {10^{ - 19}}coulombs\].

(iii) Size of a bacteria is \[0.0000005m\].

Ans: A number is in the standard form, if it is written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number. 

Size of a bacteria is \[0.0000005m\].

As we move the decimal from left to right then the power of 10 increases with a negative sign.

Therefore,

Size of a bacteria can be written as,

\[0.0000005m = 5 \times {10^{ - 7}}m\].

(iv) Size of a plant cell is \[0.00001275m\].

Ans: A number is in the standard form, if it is written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number. 

Size of a plant cell is \[0.00001275m\].

As we move the decimal from left to right then the power of 10 increases with a negative sign.

Therefore,

Size of a plant cell can be written as,

\[0.00001275m = 1.275 \times {10^{ - 5}}\].

(v) Thickness of a thick paper is \[0.07mm\].

Ans: A number is in the standard form, if it is written in the form $a \times {10^b}$ where $a$ is any natural or decimal number and $b$ is any whole number. 

Thickness of a thick paper is \[0.07mm\].

As we move the decimal from left to right then the power of 10 increases with a negative sign.

Therefore,

Thickness of a thick paper can be written as,

\[0.07mm = 7 \times {10^{ - 2}}\] .

4. In a stack there are 5 books each of thickness \[20mm\]  and 5 paper sheets each of thickness \[0.016mm\]. What is the total thickness of the stack?

Ans: There are a total of 5 books.

Thickness of each book is \[20mm\].

Therefore, total thickness of book can be calculated as,

\[ {\text{Total thickness of 5 books}}=5 \times 20mm \] 

\[ {\text{Total thickness of 5 books}}= 100mm \]

There are a total of 5 paper sheets.

Thickness of each paper sheet is \[0.016mm\].

Therefore, total thickness of paper sheets can be calculated as,

Total thickness of 5 paper sheets \[ = 5 \times 0.016mm\]

\[ = 0.08mm\]

So, the total thickness of stack

= Thickness of 5 books  +  Thickness of 5 paper sheets

Thickness of 5 books  +  Thickness of 5 paper sheets = (100 + 0.08)mm

= 100.08mm

= 1.0008 × 102mm

Thus, the total thickness of the stack is 1.0008 × 102mm.


Conclusion

Class 8 Chapter 10 Exercise 10.2 helps students how to understand and apply exponents and powers effectively. Students learn to compare large and small numbers, apply exponents to express little numbers and write numbers in standard form by completing these tasks. These skills are necessary for resolving difficult calculations and recognising mathematical symbols. Vedantu's professional solutions will make these topics simple to understand, making sure students have an excellent basis for handling exponents and powers confidently.


Class 8 Maths Chapter 10: Exercises Breakdown

Exercise

Number of Questions

Exercise 10.1

7 Questions with Solutions


CBSE Class 8 Maths Chapter 10 Other Study Materials


Chapter-Specific NCERT Solutions for Class 8 Maths

Given below are the chapter-wise NCERT Solutions for Class 8 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.



Important Related Links for CBSE Class 8 Maths

FAQs on NCERT Solutions for Class 8 Maths Chapter 10 - Exponents and Powers Exercise 10.2

1. Where can I get the NCERT Class 8 Maths Chapter 10 Exercise 10.2 Solutions?

Vedantu, offers NCERT Class 8 Maths Chapter 10 Exercise 10.2 Solutions Exponents and Powers was developed by highly qualified and experienced teachers in accordance with the most recent CBSE criteria. The solution includes exact solutions to every one in the class 8 NCERT Maths textbook. On an official website, you make quickly and gratis download PDF versions of the study guides.

2. Is Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.2 are important?

Yes, Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.2 is crucial. You can use this as a foundation for your upcoming classes as well as for any competitive exams. Students should pay special attention to this chapter and comprehend the topics. You can look to Vedantu for chapter 10 exponent and power complete and step by step solution in a free PDF format. Additionally, you will be able to increase your understanding and Discover a new method for resolving the triangle and properties problems.

3. What are the topics discussed in Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.2?

The topics discussed in Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.2 are related to power with negative exponents, law of concepts, law of exponents, exponent are negative, they also add numbers in standard form, we convert them into numbers with the same exponents.

4. Why should I choose solutions for NCERT Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.2 prepared by Vedantu?

Vedantu is a group of highly skilled teachers who have thorough understanding of the latest CBSE curriculum and years of experience in the field. Being involved in their academic community enables us to develop study materials that are up to the CBSE level and meet the needs of students. Our chapter by chapter study guides for, like the NCERT Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.2, are updated frequently and include detailed solutions to every exercise. It enables students to develop efficient shortcut techniques to solve problems with few to know errors and to complete and write your problems with ease.

5. Does Maths Class 8 Chapter 10 Exercise 10.2 Exponents and Powers requirement to practice every question?

To get good grades, you must undoubtedly practice on all of the questions from the NCERT textbook. The Class 8 Maths NCERT Solutions Chapter 10 Exercise 10.2 are the most helpful source since they provide a variety of questions that need the right concept and understanding to be solved. You can get ready for any challenging or uncommon exam questions by constantly practising and for free with comprehensive answers, step by step and see Arti solutions for all math chapters.

6. What is the main focus of Class 8 Maths NCERT Solutions Chapter 10 Exercise 10.2?

Class 8 Maths NCERT Solutions Chapter 10 Exercise 10.2 focuses on understanding and applying the rules of exponents and powers. It includes comparing large and small numbers, expressing small numbers with exponents, and writing numbers in standard form. This exercise helps students simplify complex calculations and understand the practical use of exponents in real-life scenarios.

7. How do exponents help in comparing large and small numbers in Class 8 Maths NCERT Solutions Chapter 10 Exercise 10.2?

In Maths Class 8 Chapter 10 Exercise 10.2, Exponents make it easier to compare large and small numbers by representing them in a simpler form. For example, $10^{6}$  is much larger than $10^{3}$ , and $10^{-6}$  is much smaller than $10^{-3}$. This helps in quickly understanding and comparing the magnitude of numbers.

8. What is the use of exponents in expressing small numbers in NCERT Solutions For Class 8 Maths Chapter 10 Exercise 10.2?

Exponents are used to express small numbers in a compact form, making them easier to read and write. For example, 0.000001 can be written as $1\times 10^{-3}$. This representation is particularly useful in scientific calculations where very small values are common.

9. How do you write numbers in standard form using exponents in NCERT Solutions For Class 8 Maths Chapter 10 Exercise 10.2?

To write a number in standard form using exponents, you express it as $a\times 10^{n}$, where $1\leq a< 10$ and n is an integer. For example, 4500 can be written as $4.5\times 10^{3}$. This form simplifies the number and makes it easier to handle in calculations.

10. Why is it important to learn about exponents and powers in NCERT Solutions For Class 8 Maths Chapter 10 Exercise 10.2?

Learning about exponents and powers is important because they are fundamental concepts in mathematics that are widely used in various fields, such as science, engineering, and finance. Understanding these concepts helps in simplifying complex calculations and solving problems more efficiently.

11. What are the rules for multiplying and dividing exponents in NCERT Solutions For Class 8 Maths Chapter 10 Exercise 10.2?

When multiplying exponents with the same base, you add the exponents: $a^{m}\times a^{n}=a^{m+n}$. When dividing exponents with the same base, you subtract the exponents: $a^{m}\div  a^{n}=a^{m-n}$. These rules help simplify expressions involving exponents.