Exercise 10.2 (Revised) - Chapter 12 - Exponents & Powers - Ncert Solutions class 8 - Maths

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Chapter 10: Exponents & Powers - NCERT Solutions for Class 8 Maths

Ex 10.2 Question 1.

Express the following numbers in standard form:
(i) 0.0000000000085
(ii) 0.00000000000942
(iii) 6020000000000000
(iv) 0.00000000837
(v) 31860000000

Answer.

(i) 0.0000000000085
$
=0.0000000000085 \times \frac{10^{12}}{10^{12}}=8.5 \times 10^{-12}
$
(ii) 0.00000000000942
$
=0.00000000000942 \times \frac{10^{12}}{10^{12}}=9.42 \times 10^{-12}
$
(iii) 6020000000000000
$
=6020000000000000 \times \frac{10^{15}}{10^{15}}=6.02 \times 10^{15}
$
(iv) 0.00000000837

$
=0.00000000837 \times \frac{10^9}{10^9}=8.37 \times 10^{-9}
$
(v) 31860000000

$
=31860000000 \times \frac{10^{10}}{10^{10}}=3.186 \times 10^{10}
$
Ex 10.2 Question 2.

Express the following numbers in usual form:
(i) $3.02 \times 10^{-6}$
(ii) $4.5 \times 10^4$
(iii) $3 \times 10^{-8}$
(iv) $1.0001 \times 10^9$
(v) $5.8 \times 10^{12}$
(vi) $3.61492 \times 10^6$

Answer.

(i)
(ii) $4.5 \times 10^4=4.5 \times 10000=45000$
(iii) $3 \times 10^{-8}=\frac{3}{10^8}=0.00000003$
(iv) $1.0001 \times 10^9=1000100000$
(v) $5.8 \times 10^{12}=5.8 \times 1000000000000$

$
=5800000000000
$
(vi) $3.61492 \times 10^6=3.61492 \times 1000000$
$
=3614920
$
Ex 10.2 Question 3.

Express the number appearing in the following statements in standard form:
(i)1 micron is equal to $\frac{1}{1000000} \mathrm{~m}$.

(ii) Charge of an electron is $0.000,000,000,000,000,000,16$ coulomb.
(iii) Size of a bacteria is $0.0000005 \mathrm{~m}$.
(iv) Size of a plant cell is
$0.00001275 \mathrm{~m}$.
(v) Thickness if a thick paper is $0.07 \mathrm{~mm}$.

Answer.

(i) 1 micron
$
=\frac{1}{1000000}=\frac{1}{10^6}=1 \times 10^{-5} \mathrm{~m}
$
(ii)Charge of an electron is
0.00000000000000000016 coulombs.
$=0.00000000000000000016 \times \frac{10^{19}}{10^{19}}$
$
=1.6 \times 10^{-19} \text { coulomb }
$
(iii) Size of bacteria $=0.0000005$
$
\frac{5}{10000000}=\frac{5}{10^7}=5 \times 10^{-7} \mathrm{~m}
$
(iv) Size of a plant cell is $0.00001275 \mathrm{~m}$

$
=0.00001275 \times \frac{10^5}{10^5}=1.275 \times 10^{-5} \mathrm{~m}
$
(v) Thickness of a thick paper $=0.07 \mathrm{~mm}$
$
=\frac{7}{100} \mathrm{~mm}=\frac{7}{10^2}=7 \times 10^{-2} \mathrm{~mm}
$
Ex 10.2 Question 4.

In a stack there are 5 books each of thickness $20 \mathrm{~mm}$ and 5 paper sheets each of thickness $0.016 \mathrm{~mm}$. What is the total thickness of the stack?

Answer.

Thickness of one book $=20 \mathrm{~mm}$
Thickness of 5 books $=20 \times 5=100 \mathrm{~mm}$
Thickness of one paper $=0.016 \mathrm{~mm}$
Thickness of 5 papers $=0.016 \times 5$
$=0.08 \mathrm{~mm}$
Total thickness of a stack $=100+0.08$
$=100.08 \mathrm{~mm}$
$=100.08 \times \frac{10^2}{10^2}$
$=1.0008 \times 10^2 \mathrm{~mm}$