NCERT Solutions for Class 8 Maths Chapter 10 Exponents And Powers Ex 10.2

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.

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