What do you understand by scientific notation?
Scientific notation/Standard form:
In scientific notation, a number is expressed as some power of ten multiplied by a number between 1 and 10.
Examples:
- The Moon is 384000000 meters away from the Earth. The distance of the moon from the Earth can also be expressed as 3.84 x 108 This saves writing down or interpreting large numbers of zeros.
- A number 62750 can be expressed as 6.275 x 104. Similarly, the standard form of 0.00045 is 4.5 x 10-4
Quick Quiz
1. Name five prefixes most commonly used.
Ans: (1) kilo (k) = 103 (2) centi(c)10-2 (3) milli(m) = 10-3
(4) micro (u) = 10-6 (5) mega (M) = 106
2.The Sun is one hundred and fifty million kilometres away from the Earth. Write this.
(a) as an ordinary whole number
(b) In scientific notation.
Ans: The distance of Sun from the Earth = 150 million km
(A) as an ordinary whole number:
= 150 x 106km= 150 x 106 x 103m 1 million 106 1 kilo = 103
= 150000000000 m
(B) In scientific notation.
= 150 x 106 x 103
= 150 x 109
= 15 x 10 x 109
= 15 x 1010
= 15 ÷ 10 x 10 x 1010
=1.5 x 1011
=1.5 x 1011 m
3. Write the numbers given below in scientific notation.
- 3000000000 ms-1C.6400000 m
- 0000000016 g D. 0.0000548 s
Ans:
A. 3000000000 ms-1
= 3 x 1000000000 ms-1
= 3x 109 ms-1
B. 6400000 m
= 64 x 105m
= 6.4 x 10 x 105
= 6.4 x 106m
C. 0000000016 g
= 0.0000000016 ÷ 10000000000 g
= 16 x 10-10g
=1.6x 10x 10-10g
=1.6x10-9g
D. 0.0000548 s
= 0.0000548
= 0.0000548 ÷10000000
= 548 x 10-7
= 5.48 x 102 x 10-7
=5.48x 10-5 s
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