Page 76 - ICSE Math 7

Example 14: Find the number from each of the following expanded forms.
5
1
(a) 5 × 10 + 5 × 10 + 5 × 10 0
4
2
3
1
(b) 3 × 10 + 6 × 10 + 0 × 10 + 4 × 10 + 5 × 10 0
0
5
1
Solution: (a) 5 × 10 + 5 × 10 + 5 × 10 = 5,00,000 + 50 + 5 = 5,00,055
2
1
4
3
(b) 3 × 10 + 6 × 10 + 0 × 10 + 4 × 10 + 5 × 10 0
= 30,000 + 6,000 + 0 + 40 + 5 = 36,045
Example 15: Express the following numbers in standard form.
(a) 2,00,00,000 (b) 39,087.8 (c) 0.00000000000017
Solution: (a) 2,00,00,000 = 2.0 × 1,00,00,000 = 2.0 × 10 7
(b) 3,9087.8 = 3.90878 × 10,000 = 3.90878 × 10 4
(c) 0.00000000000017 = 1.7 × 0.0000000000001 = 1.7 × 10 –13
Example 16: Express the number appearing in the following statements in scientific or standard form.
(a) The approximate distance between the earth and the moon is 384,000,000 m.
(b) The approximate diameter of the sun is 1,400,000,000 m.

(c) In a galaxy there are on an average 100,000,000,000 stars.
(d) The universe is estimated to be about 12,000,000,000 years old.
8
Solution: (a) 384,000,000 m = 3.84 × 100,000,000 m = 3.84 × 10 m
9
(b) 1,400,000,000 m = 1.4 × 1,000,000,000 = 1.4 × 10 m
11
(c) 100,000,000,000 = 1 × 100,000,000,000 = 1 × 10 stars
10
(d) 12,000,000,000 years = 1.2 × 10,000,000,000 = 1.2 × 10 years
Example 17: Compare the following numbers:
8
12
5
(a) 1.7 × 10 ; 8.5 × 10 (b) 9.8 × 10 ; 1.3 × 10 6
Solution: (a) These numbers are in standard form. Therefore, we just need to compare the powers
12
8
of 10. The power of 10 is greater in 1.7 × 10 in comparison to 8.5 × 10 .
12
8
∴ 1.7 × 10 > 8.5 × 10 .
(b) Since the numbers are in standard form, the number having greater power of 10 is
5
6
greater. ∴ 9.8 × 10 < 1.3 × 10 .
17
Example 18: The mass of a particle is 3.84 × 10 grams. Find the mass of a particle 5,000 times
heavier than it.
17
Solution: Mass of a particle = 3.84 × 10 grams
17
Mass of a particle 5,000 times heavier = 3.84 × 10 × 5,000 grams
3
21
17
= (3.84 × 10 ) × (5 × 10 ) = 19.2 × 10 17 + 3 = 1.92 × 10 grams
13
Example 19: The star Sirius is about 8.1 × 10 km from the earth. Assuming that light travels at
5
–1
3.0 × 10 km s , find how long does light take to reach the earth from Sirius?
5
Solution: Speed of light = 3.0 × 10 km s –1
13
Distance given = 8.1 × 10 km
Distance 8.1 × 10 13 13 – 5 8
Time = = sec = 2.7 × 10 sec = 2.7 × 10 sec
Speed 3.0 × 10 5
3
Now 1 hr = (60 × 60) sec or 3,600 sec = 3.6 × 10 sec
4
8
5
\ 2.7 × 10 sec = 2.7 × 10 8 or 0.75 × 10 hours = 7.5 × 10 hours
3.6 × 10 3
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