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\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

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Mercury = 57900000 km = 5.79 × 10 km
Neptune = 4497000000 km = 4.497 × 10 km create and solve
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Saturn = 1427000000 km = 1.427 × 10 km A large library has a collection of
25,000,000 books. Based on this
Uranus = 2870000000 km = 2.87 × 10 km information, make a question on the
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Venus = 108200000 km = 1.082 × 10 km standard form of a number.
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(b) Order of planets from closest to the sun to farthest from the sun is,

Mercury < Venus < Earth < Mars < Jupiter < Saturn < Uranus < Neptune.
Example 11: Express the following numbers in usual form.

(a) 1.45 × 10 11 (b) 2 × 10 16 (c) 4.165642 × 10 8 (d) 3.00009 × 10 –11
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Solution: (a) 1.45 × 10 = 1.45 × 100000000000 = 145000000000
(b) 2 × 10 = 2 × 10000000000000000 = 20000000000000000
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(c) 4.165642 × 10 = 4.165642 × 100000000 = 416564200
. 3 00009 300009
(d) 3.0000 9 10 − 11 = = = = 0 0000000000300009
.
×
100000000000 10000000000000000
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Example 12: If the mass of the Earth is 5.97 × 10 kg and the mass of the Moon is 7.35 × 10 kg,
which is heavier and by how much?
Solution: Here, we have to compare the mass of the Earth and the Moon. We will convert them
into numbers with the same exponents 22, as 22 < 24.
22
22
24
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Mass of Earth = 5.97 × 10 kg = 5.97 × 100 × 10 = 597 × 10 kg; Mass of Moon = 7.35 × 10 kg
Since, 597 × 10 kg > 7.35 × 10 kg. So, Earth is heavier than Moon.
22
22
22
22
22
Further, the difference of masses = (597 × 10 kg) – (7.35 × 10 kg) = (597 – 7.35) × 10 kg
= 589.65 × 10 kg = 5.8965 × 10 kg
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22
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Hence, the Earth is heavier than the Moon by 5.8965 × 10 kg.
Practice Time 11C
1. Write the following numbers in standard form.

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(a) 4.7865 × 10 × 10 3 (b) 999 × 10 (c) 0.00100001 × 10 8 (d) 8020000000000000
2. Express the following numbers in usual form.
(a) 7 × 10 11 (b) 5.651672 × 10 6 (c) 2.0000002 × 10 –10
3. Express the following measurements in standard form.

(a) Thickness of a paper is 0.05 mm.
(b) Number of stars in a galaxy is 100 billion.
(c) Distance from the Earth to the Moon is 384317695 m.
(d) Size of a plant cell is 0.00001275 m.
4. The mass of a proton is 1.67 × 10 –24 g and that of an electron is 9.10 × 10 –28 g. What is the total mass?

5. A particular star is at a distance of about 8.1 × 10 km from the Earth. Assuming that light travels
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at 3 × 10 m/s, find how long does light take from that star to reach the Earth.
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Mathematics-8 272