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Example 20: Express the following numbers in the standard form:

(a) 57,800,000,000 (b) 68,312,620,000,000,000

(c) 32107.34

Solution: (a) 57,800,000,000 = 5.78 × 10,000,000,000 = 5.78 × 10 10
(b) 68,312,620,000,000,000 = 6.831262 × 10,000,000,000,000,000 = 6.831262 × 10 16

(c) 32107.34 = 3.210734 × 10000 = 3.210734 × 10 4

In converse, we can write standard form of a large number into its usual form too.
Example 21: Express the following numbers in usual form:
(a) 3.2 × 10 3 (b) 9.81 × 10 5 (c) 1.231 × 10 7

3
Solution: (a) 3.2 × 10 = 3.2 × 1000 = 3200
5
(b) 9.81 × 10 = 9.81 × 100000 = 981000
7
(c) 1.231 × 10 = 1.231 × 10000000 = 12310000
Practice Time 4C

1. Write each of the following in short form.
4
3
2
1
(a) 8 ×10 + 6 ×10 + 0 × 10 + 4 × 10 + 5 × 10 0
3
(b) 4 × 10 + 5 × 10 + 3 × 10 + 2 × 10 0
2
5
(c) 3 × 10 + 7 × 10 + 5 × 10 0
4
2
(d) 9 × 10 + 2 × 10 + 3 × 10 1
2
5
2. Express the following numbers in their standard form.
(a) 109,852,000 (b) 14,539,500,000
(c) 125,403,000,000 (d) 283,124,000,000,000
(e) 53154.547
3. Express the following information in the standard form.

(a) The distance of the moon from the earth is 384,400,000 m.
(b) Mass of Uranus is 86,800,000,000,000,000,000,000,000 kg

(c) The mass of the moon is 73,480,000,000,000 000,000,000 kg.
(d) Speed of light in vacuum is 300,000,000 m/s.

(e) Diameter of the Sun is 1,400,000,000 m.
4. Express the following information in usual form.

6
(a) The diameter of the Sun is 1.39 × 10 km.
7
(b) The diameter of the Earth is 1.274 × 10 m.
8
(c) Speed of light is 3 × 10 m/sec.
8
(d) The distance between the Sun and the Earth is 1.5 × 10 km.

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