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### Week Ending September 02 2011

posted Sep 1, 2011, 4:46 PM by Frania Lugo   [ updated Sep 16, 2011, 9:30 AM ]
This week I learned about scientific notation. Scientific notation is used by scientist and everyday people to show really big numbers or really small numbers. Can you imagine instead of writing 0.0000000056, we write 5.6 x 10-9. Are you wondering how this works yet?
Check that all exponents you are adding/subtracting are the same
IF the exponents are not the same you must choose which one to change (its recommended to                                                                   use the one that is bigger)
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
(two significant figures)

Multiplication:
The digit are multiplied in the Normal way and the exponents are ADDED.
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 x 10-2
(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: (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)

Converting:
converting is used to make one measurement go from one unit to another like converting hours to minutes and that wouldn't be possible with out conversions. When converting you must first look at what unit you have and what you are converting it to. make sure that the unit you want to get rid of goes on top on the first space and than you put in on the bottom
example:
In the image below i want to get rid of lbs so i put lbs my STARTING unit he first set of parenthesis on the bottom to make sure they cancel out. The numbers on the top multiply and those in the bottom divide.
How to know where the units go?
Prexis Symbol Factor
yotta Y 1024 = 1,000,000,000,000,000,000,000,000
zetta Z 1021 = 1,000,000,000,000,000,000,000
exa E 1018 = 1,000,000,000,000,000,000
peta P 1015 = 1,000,000,000,000,000
tera T 1012 = 1,000,000,000,000
giga G 109 = 1,000,000,000
mega M 106 = 1,000,000
kilo k 103 = 1,000
hecto h 102 = 100
deka da 101 = 10
deci d 10-1 = 0.1
centi c 10-2 = 0.01
milli m 10-3 = 0.001
micro µ 10-6 = 0.000,001
nano n 10-9 = 0.000,000,001
pico p 10-12 = 0,000,000,000,001
femto f 10-15 = 0.000,000,000,000,001
atto a 10-18 = 0.000,000,000,000,000,001
zepto z 10-21 = 0.000,000,000,000,000,000,001
yocto y 10-24 = 0.000,000,000,000,000,000,000,001

This video better explains how to convert units of measurement