What is scientific notation, ....?( 10 points)

scientific notation = 科學記數法
http://en.wikipedia.org/wiki/Scientific_notation

eates: 你係咪問rate呀...(http://en.wikipedia.org/wiki/Rate)

ratios: A ratio is a quantity that denotes the proportional amount or magnitude of one quantity relative to another...(http://en.wikipedia.org/wiki/Ratio)

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p.s. 可唔可以問得具體少少, 你想知道邊方面的知識

Scientific notation is a way to make numbers easier to work with. In scientific notation, you move the decimal place until you have a number between 1 and 10. Then you add a power of ten that tells how many places you moved the decimal.
EXAMPLE~~~
*************Scientific notation can be used to turn 0.0000073 into 7.3 x 10-6.**********
HOW????
First, move the decimal place until you have a number between 1 and 10. If you keep moving the decimal point to the right in 0.0000073 you will get 7.3.
Next, count how many places you moved the decimal point. You had to move it 6 places to the right to change 0.0000073 to 7.3. You can show that you moved it 6 places to the right by noting that the number should be multiplied by 10-6.
7.3 x 10-6 = 0.0000073

REMEMBER: in a power of ten, the exponent—the small number above and to the right of the 10—tells which way you moved the decimal point.

A power of ten with a positive exponent, such as 105, means the decimal was moved to the left.
A power of ten with a negative exponent, such as 10-5, means the decimal was moved to the right.

Powers of Ten
BILLIONS
109 = 1,000,000,000
10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000,000
MILLIONS
106 = 1,000,000
10 x 10 x 10 x 10 x 10 x 10 = 1,000,000
HUNDRED THOUSANDS
105 = 100,000
10 x 10 x 10 x 10 x 10 = 100,000
TEN THOUSANDS
104 = 10,000
10 x 10 x 10 x 10 = 10,000
THOUSANDS
103 = 1,000
10 x 10 x 10 = 1,000
HUNDREDS
102 = 100
10 x 10 = 100
TENS
101 = 10
ONES
100 = 1
TENTHS
10–1 = 1/10
1/10 = 0.1
HUNDREDTHS
10–2 = 1/102
1/102 = 0.01
THOUSANDTHS
10–3 = 1/103
1/103 = 0.001
TEN THOUSANDTHS
10–4 = 1/104
1/104 = 0.0001
HUNDRED THOUSANDTHS
10–5 = 1/105
1/105 = 0.00001
MILLIONTHS
10–6 = 1/106
1/106 = 0.000001
BILLIONTHS
10–9 = 1/109
1/109 = 0.000000001


Addition and Subtraction:

All numbers are converted to the same power of 10, and the digit terms are added or subtracted.
Example: (4.215 x 10-2) + (3.2 x 10-4) = (4.215 x 10-2) + (0.032 x 10-2) = 4.247 x 10-2
Example: (8.97 x 104) - (2.62 x 103) = (8.97 x 104) - (0.262 x 104) = 8.71 x 104

Multiplication:

The digit terms are multiplied in the normal way and the exponents are added. The end result is changed so that there is only one nonzero digit to the left of the decimal.
Example: (3.4 x 106)(4.2 x 103) = (3.4)(4.2) x 10(6+3) = 14.28 x 109 = 1.4 x 1010
(to 2 significant figures)
Example: (6.73 x 10-5)(2.91 x 102) = (6.73)(2.91) x 10(-5+2) = 19.58 x 10-3 = 1.96 x10-2(to 3 significant figures)

Division:

The digit terms are divided in the normal way and the exponents are subtracted. The quotient is changed (if necessary) so that there is only one nonzero digit to the left of the decimal.
Example: (6.4 x 106)/(8.9 x 102) = (6.4)/(8.9) x 10(6-2) = 0.719 x 104 = 7.2 x 103
(to 2 significant figures)
Example: (3.2 x 103)/(5.7 x 10-2) = (3.2)/(5.7) x 103-(-2) = 0.561 x 105 = 5.6 x 104
(to 2 significant figures)

Powers of Exponentials:

The digit term is raised to the indicated power and the exponent is multiplied by the number that indicates the power.
Example: (2.4 x 104)3 = (2.4)3 x 10(4x3) = 13.824 x 1012 = 1.4 x 1013
(to 2 significant figures)
Example: (6.53 x 10-3)2 = (6.53)2 x 10(-3)x2 = 42.64 x 10-6 = 4.26 x 10-5
(to 3 significant figures)