RS Aggarwal solution class 8 chapter 2 Exponents Exercise 2B

Exercise 2B

Page-36

Q1 | Ex-2B | Exponents | Class 8 | RS AGGARWAL | Chapter 2 | myhelper

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Question 1:

Write each of the following numbers in standard form:
(i) 57.36
(ii) 3500000
(iii) 273000
(iv) 168000000
(v) 4630000000000
(vi) 345 × 10⁵

Answer 1:

(i) $57.36=5.736\times 10$
(ii) $3500000=3.5\times {10}^6$
(iii) $273000=2.73\times {10}^5$
(iv) $168000000=1.68\times {10}^8$
(v) $4630000000000=4.63\times {10}^{12}$
(vi) $345\times {10}^5=3.45\times {10}^7$

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Question 2:

Write each of the following numbers in usual form:
(i) 3.74 × 10⁵
(ii) 6.912 × 10⁸
(iii) 4.1253 × 10⁷
(iv) 2.5 × 10⁴
(v) 5.17 × 10⁶
(vi) 1.679 × 10⁹

Answer 2:

(i) $3.74 \times 10^{5}=\frac{374}{100} \times 10^{5}=\frac{374 \times 10^{5}}{10^{2}}$ $=374 \times 10^{(5-2)}=374 \times 10^{3}$

=374000

(ii) $6.912 \times 10^{8}=\frac{6912}{1000} \times 10^{8}=\frac{6912 \times 10^{8}}{10^{3}}$ $=6912 \times 10^{(8-3)}=6912 \times 10^{5}$

=691200000

(iii) $4.1253 \times 10^{7}=\frac{41253}{10000} \times 10^{7}$ $=\frac{41253 \times 10^{7}}{10^{4}}=41253 \times 10^{(7-4)}=41253 \times 10^{3}$

=41253000

(iv) $2.5 \times 10^{4}=\frac{25}{10} \times 10^{4}$ $=\frac{25 \times 10^{4}}{10}=25 \times 10^{(4-1)}=25 \times 10^{3}$

=25000

(v) $5.17 \times 10^{6}=\frac{517}{100} \times 10^{6}$ $=\frac{517 \times 10^{6}}{10^{2}}=517 \times 10^{(6-2)}=517 \times 10^{4}$

=5170000

(vi) $1.679 \times 10^{9}=\frac{1679}{1000} \times 10^{9}$ $=\frac{1679 \times 10^{9}}{10^{9}}=1679 \times 10^{(9-3)}=1679 \times 10^{6}$

=1679000000

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Question 3:

(i) The height of Mount Everest is 8848 m. Write it in standard form.
(ii) The speed of light is 300000000 m/sec. Express it in standard form.
(iii) The distance from the earth to the sun is 149600000000 m. Write it in standard form.

Answer 3:

(i) The height of the Mount Everest is 8848 m.
In standard form, we have:
​$8848=8.848\times 1000 \mathrm{m}=8.848\times {10}^3\mathrm{m}$.

(ii) The speed of light is 300000000 m/s.
In standard form, we have: 
$300000000=3\times 100000000 \mathrm{m}/\mathrm{s}=3\times {10}^8 \mathrm{m}/\mathrm{s}$

(iii) The Sun$-$Earth distance is 149600000000 m.
In standard form, we have: 

149600000000=1496×100000000

=1.496×1000×100000000

$=1.496 \times 10^{3} \times 10^{8}=1.496 \times 10^{11}$ m

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Question 4:

Mass of earth is (5.97 × 10²⁴) kg and mass of moon is (7.35 × 10²²) kg. What is the total mass of the two?

Answer 4:

Mass of the Earth = $5.97\times {10}^{24} \mathrm{kg}$

Now, $=5.97 \times 10^{24}=5.97 \times 10^{(2+22)}$
$=5.97 \times 10^{2} \times 10^{22}$
$=597 \times 10^{22}$

So, the mass of the Earth can also be written as $597\times {10}^{22} \mathrm{kg}$.

Mass of the Moon = $7.35\times {10}^{22} \mathrm{kg}$

Sum of the masses of the Earth and the Moon:
$=\left(597 \times 10^{22}\right)+\left(7.35 \times 10^{22}\right)$ 

$=(597+7.35) \times 10^{22}$

$=604.35 \times 10^{22} \mathrm{~kg}$

$=6.0435 \times 100 \times 10^{22}$

$=6.0435 \times 10^{2} \times 10^{22}$

$=6.0435 \times 10^{(2+22)}$

$=6.0435 \times 10^{24} \mathrm{~kg}$

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Question 5:

Write each of the following numbers in standard form:
(i) 0.0006
(ii) 0.00000083
(iii) 0.0000000534
(iv) 0.0027
(v) 0.00000165
(vi) 0.00000000689

Answer 5:

(i) $0.0006$$=\frac{6}{10^{4}}=6 \times 10^{-4}$

(ii) $0.00000083$$=\frac{83}{10^{8}}=\frac{8.3 \times 10}{10^{8}}$ $=8.3 \times 10^{(1-8)}=8.3 \times 10^{-7}$

(iii) $0.0000000534$$=\frac{534}{10^{10}}=\frac{5.34 \times 10^{2}}{10^{10}}$ $=5.34 \times 10^{(2-10)}=5.34 \times 10^{-8}$

(iv) $0.0027$$=\frac{27}{10^{4}}=\frac{2.7 \times 10}{10^{4}}$ $=2.7 \times 10^{(1-4)}=2.7 \times 10^{-3}$

(v) 0.00000165$=\frac{165}{10^{3}}=\frac{1.65 \times 10^{2}}{10^{3}}$ $=1.65 \times 10^{(2-8)}=1.65 \times 10^{-6}$

(vi) 0.00000000689 $=\frac{689}{10^{11}}=\frac{6.89 \times 10^{2}}{10^{11}}$ $=6.89 \times 10^{(2-11)}=6.89 \times 10^{-9}$

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Question 6:

(i) 1 micron = $\frac{1}{1000000}$ m. Express it in standard form.
(ii) Size of a bacteria = 0.0000004 m. Express it in standard form.
(iii) Thickness of a paper = 0.03 mm. Express it in standard form.

Answer 6:

(i) $1 \mathrm{micron} = \frac{1}{1000000} \mathrm{m}=1\times {10}^{-6} \mathrm{m}$

(ii) $0.0000004 \mathrm{m}=\frac{4}{{10}^7}\mathrm{m}=\left(4\times {10}^{-7}\right) \mathrm{m}$

(iii) $\mathrm{Thickness} \mathrm{of} \mathrm{paper} = 0.03 \mathrm{mm}$

$=\frac{3}{10^{2}} \mathrm{~mm}=\left(3 \times 10^{-2}\right) \mathrm{mm}$

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Question 7:

Write each of the following numbers in usual form:
(i) 2.06 × 10⁻⁵
(ii) 5 × 10⁻⁷
(iii) 6.82 × 10⁻⁶
(iv) 5.673 × 10⁻⁴
(v) 1.8 × 10⁻²
(vi) 4.129 × 10⁻³

Answer 7:

(i) $2.06 \times 10^{-5}=\frac{206}{100} \times \frac{1}{10^{5}}=\frac{206}{10^{2} \times 10^{5}}$ $=\frac{206}{10^{(5+2)}}=\frac{206}{10^{7}}=\frac{206}{10000000}$

=0.0000206

(ii) $5 \times 10^{-7}=\frac{5}{10^{7}}=\frac{5}{10000000}$

$=0.0000005$

(iii) $6.82 \times 10^{-6}=\frac{682}{100} \times \frac{1}{10^{6}}=\frac{682}{10^{2} \times 10^{6}}$ $=\frac{682}{10^{(2+6)}}=\frac{682}{10^{8}}=\frac{682}{100000000}$

=0.00000682

(iv) $5.673 \times 10^{-4}=\frac{5673}{1000} \times \frac{1}{10^{4}}=\frac{5673}{10^{3} \times 10^{4}}$ $=\frac{5673}{10^{(3+4)}}=\frac{5673}{10^{7}}=\frac{5673}{10000000}$

$=0.0005673$

(v) $1.8 \times 10^{-2}=\frac{18}{10} \times \frac{1}{10^{2}}=\frac{18}{10 \times 10^{2}}$ $=\frac{18}{10^{(1+2)}}=\frac{18}{10^{3}}=\frac{18}{1000}$

=0.018

(vi) $4.129 \times 10^{-3}=\frac{4129}{1000} \times \frac{1}{10^{3}}=\frac{4129}{10^{3} \times 10^{3}}$ $=\frac{4129}{10^{(3+3)}}=\frac{4129}{10^{6}}=\frac{4129}{1000000}$

=0.004129