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Q.4.    Express the number appearing in the following statements in standard form.

(a) The distance between Earth and Moon is 384,000,000 m.

(b) Speed of light in vacuum is 300,000,000 m/s.

(c) Diameter of the Earth is 1,27,56,000 m.

(d) Diameter of the Sun is 1,400,000,000 m.

(e) In a galaxy there are on an average 100,000,000,000 stars.

(f) The universe is estimated to be about 12,000,000,000 years old.

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.

(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.

(i) The earth has 1,353,000,000 cubic km of sea water.

(j) The population of India was about 1,027,000,000 in March, 2001.

(a) The distance between Earth and Moon = 384,000,000 m                                                                                                                                                                                                                     (b) Speed of light in vacuum =300,000,000 m/s.                                                                                 ...

Q.3.    Express the following numbers in standard form:

(i) 5,00,00,000      (ii) 70,00,000     (iii) 3,18,65,00,000    (iv) 3,90,878     (v) 39087.8     (vi) 3908.78

(i) 5,00,00,000        (ii) 70,00,000    (iii) 3,18,65,00,000                                                              (iv) 3,90,878                  (v) 39087.8                               (vi) 3908.78

Q.2.    Find the number from each of the following expanded forms:

$(a)\: 8\times 10^{4}+6\times 10^{3}+0\times 10^{2}+4\times 10^{1}+5\times 10^{0}$

$(b)\: 4\times 10^{5}+5\times 10^{3}+3\times 10^{2}+2\times 10^{0}$

$(c)\: 3\times 10^{4}+7\times 10^{2}+5\times 10^{0}$

$(d)\: 9\times 10^{5}+2\times 10^{2}+3\times 10^{1}$

Thus, the above problems are simplified in simpler forms.

Q.1.    Write the following numbers in the expanded forms:

279404, 3006194, 2806196, 120719, 20068

(i)  279404                       (ii) 3006194                 (iii) 2806196                             (IV)  120719                 (V)  20068

Expand by expressing powers of 10 in the exponential form:

(i) 172      (ii) 5,643    (iii) 56,439    (iv) 1,76,428

(i) 172                          (ii) 5,643                                       (iii) 56,439                                 (iv) 1,76,428

Q.5.    Simplify:

$(i)\: \frac{(2^{5})^{2}\times 7^{3}}{8^{3}\times 7}$

can be simplified as

Q.5.    Simplify:

$(iii)\: \frac{3^{5}\times 10^{5}\times 25}{5^{7}\times 6^{5}}$

can be simplified as

Q.5.    Simplify:

$(ii)\frac{25\times 5^{2}\times t^{8}}{10^{3}\times t^{4}}$

can be simplified as

Q.4.    Express each of the following as a product of prime factors only in exponential form:

$(i)\: 108\times 192$          $(ii)\: 270$        $(iii)\: 729\times 64$       $(iv)\: 768$

2 108 2 54 3 27 3 9 3 3   1   2 192 2 96 2 48 2 24 2 12 2 6 3 3   1                                    ...

$(i)\: 10\times 10^{11}=100^{11}$            $(ii)\: 2^{3}> 5^{2}$       $(iii)\: 2^{3}\times 3^{2}= 6^{5}$         $(iv)\: 3^{0}=(1000)^{0}$

can be simplified as                Since ,  Thus, it is false can be simplified as  Since, Thus, it is false can be simplified as  Since ,  Thus, it is false can be simplified as  Since, LHS = RHS Thus, it is true.

Q.2.    Simplify and express each of the following in exponential form:

$(xii)\: (2^{3}\times 2)^{2}$

can be simplified as

Q.2.    Simplify and express each of the following in exponential form:

$(xi)\: \frac{4^{5}\times a^{8}b^{3}}{4^{5}\times a^{5}b^{2}}$

can be simplified as

Q.2.    Simplify and express each of the following in exponential form:

$(x)\: (\frac{a^{5}}{a^{3}})\times a^{8}$

can be simplified as

Q.2.    Simplify and express each of the following in exponential form:

$(ix)\: \frac{2^{8}\times a^{5}}{4^{3}\times a^{3}}$

can be simplified as

Q.2.    Simplify and express each of the following in exponential form:

$(viii)\: (3^{0}+2^{0})\times 5^0$

can be simplified as

Q.2.    Simplify and express each of the following in exponential form:

$(vi)\: 2^{0}+3^{0}+4^{0}$

can be simplified as

Q.2.    Simplify and express each of the following in exponential form:

$(v)\: \frac{3^{7}}{3^{4}\times 3^{3}}$

can be simplified as

Q.2.    Simplify and express each of the following in exponential form:

$(iv)\: \frac{3\times 7^{2}\times 11^{8}}{21\times 11^{3}}$

can be simplified as

Q.2.    Simplify and express each of the following in exponential form:

$(iii)\: 25^{4}\div 5^{3}$

can be simplified as

Q.2.    Simplify and express each of the following in exponential form:

$(ii)\: ((5^{2})^{3}\times 5^{4})\div 5^{7}$

can be simplified as
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