Page 91 - Start Up Mathematics_7

Scientific Notation of Numbers
At times it becomes difficult to express very large or very small numbers in their full form. We
know that the mass of the earth is roughly 6,000,000,000,000,000,000,000,000 kg. The measure
of radius of the helium atom is 0.0000000011 mm. In fact simply looking at these figures, we
can’t even get their exact magnitudes. It is cumbersome to remember and count the number of
zeros in such numbers. Therefore, to overcome this, we use the scientific notation of a number.
n
We write very large or very small numbers in the form p × 10 , where Do you know?
p is a terminating decimal such that 1 ≤ p < 10 and n is an integer. The The scientific notation
number written in this form is said to be in scientific notation. of number is also known

Example 14: Write the following numbers in expanded form: as standard form.
2,89,704; 48,06,196; 3,10,005
5
3
4
2
1
Solution: 2,89,704 = 2 × 10 + 8 × 10 + 9 × 10 + 7 × 10 + 0 × 10 + 4 × 10 0
2
3
1
5
4
6
48,06,196 = 4 × 10 + 8 × 10 + 0 × 10 + 6 × 10 + 1 × 10 + 9 × 10 + 6 × 10 0
5
2
1
4
3
3,10,005 = 3 × 10 + 1 × 10 + 0 × 10 + 0 × 10 + 0 × 10 + 5 × 10 0
Example 15: Find the number from each of the following expanded forms:
5
1
(a) 5 × 10 + 5 × 10 + 5 × 10 0
3
2
1
4
(b) 3 × 10 + 6 × 10 + 0 × 10 + 4 × 10 + 5 × 10 0
1
0
5
Solution: (a) 5 × 10 + 5 × 10 + 5 × 10 = 5,00,000 + 50 + 5 = 5,00,055
4
3
2
1
(b) 3 × 10 + 6 × 10 + 0 × 10 + 4 × 10 + 5 × 10 0
= 30,000 + 6,000 + 0 + 40 + 5 = 36,045
Example 16: Express the following numbers in standard form:
(a) 2,00,00,000 (b) 2,18,45,00,000 (c) 39,087.8
Solution: (a) 2,00,00,000 = 2.0 × 1,00,00,000 = 2.0 × 10 7
(b) 2,18,45,00,000 = 2.1845 × 1,00,00,00,000 = 2.1845 × 10 9
(c) 3,9087.8 = 3.90878 × 10,000 = 3.90878 × 10 4
Example 17: Write each of the numbers in standard form:
(a) 500,000,000,000 (b) 0.000 000 000 000 17
Solution: (a) 500,000,000,000 = 5 × 100,000,000,000 = 5 × 10 11
(b) 0.000 000 000 000 17 = 1.7 × 0.000 000 000 000 1 = 1.7 × 10 –13
Example 18: Express the number appearing in the following statements in scientific or standard
form.
(a) The distance between the earth and the moon is 384,000,000 m.
(b) The 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.

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

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