Scientific Notation Calculations

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DRTLA

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Ok, before you call me an idiot for asking this question, realize my last math related class was 8 years ago. I am really having trouble remembering scientific notation calculations. I did a forum search, but didn't find anything answering how to do them. In the physical sciences section, every other problem seems to have it on there....so I need HELP. Can anyone explain very briefly methods to multiply, add, and subtract using scientific notation? I would greatly appreciate it.

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Ok, before you call me an idiot for asking this question, realize my last math related class was 8 years ago. I am really having trouble remembering scientific notation calculations. I did a forum search, but didn't find anything answering how to do them. In the physical sciences section, every other problem seems to have it on there....so I need HELP. Can anyone explain very briefly methods to multiply, add, and subtract using scientific notation? I would greatly appreciate it.

I totally struggled with this too.

For multiplication:

Multiply the "BIG" numbers and Add the exponents

ex: 3.0x10^-3 * 4.0x10^2

3.0 * 4.0 = 12.0

-3 + 2 = -1

12.0x10^-1

simplifies to: 1.2x10^0

For Division:

Divide the "BIG" numbers and subtract the exponents

3.0x10^-3 / 4.0x10^2

3.0 / 4.0 = .75

-3 - 2 = -5

.75x10^-5

simplifies to: 7.5x10^-6

Make sense?
 
The exponents are added/subtracted when you multiply/divide.
Exponents are multiplied/divided only when raised to powers (10^2)^3 = 10^8
 
also worthy of mentioning is the mnemonic "LARS" that was suggested in the examkrackers books.
LARS= Left Add, Right Subtract
100x10^5
LA (add to the left side), RS (subtract from the right side)
=1000x10^4

i forget the exact way they described it but thats how i do it, sometimes i'll actually write "LA" and "RS" to the side i'm doing it on because it can get kinda tricky with negative exponents.

another example from the above post:
ex: 0.75x10^-5
add to the left side, subract from right side
0.75 goes to to 7.5 (you increased the value), -5 goes to -6 (you decreased the value)
=7.5x10^-6
 
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Thank you very much. So with the LARS approach, when you simplify, you are simply moving the decimal place on spot to the right, while subtracting one from the exponent? That is the way it looks...just want to make sure I have it right. THANKS AGAIN.
 
Ok, before you call me an idiot for asking this question, realize my last math related class was 8 years ago. I am really having trouble remembering scientific notation calculations. I did a forum search, but didn't find anything answering how to do them. In the physical sciences section, every other problem seems to have it on there....so I need HELP. Can anyone explain very briefly methods to multiply, add, and subtract using scientific notation? I would greatly appreciate it.

go to your local library, borrow an elementary math book and do all the scientific notation math problems in it. It takes nothing but a little practice.
 
Thank you very much. So with the LARS approach, when you simplify, you are simply moving the decimal place on spot to the right, while subtracting one from the exponent? That is the way it looks...just want to make sure I have it right. THANKS AGAIN.

yeah, technically what they were doing was you multiply one side by ten and divide the other side by 10. but i just think of it as 'left add, right subtract' like you said. keep in mind it works the other way around! you can go 'right add, left subtract' too lol.
examples:
1) using LARS like you described:
100x10^5
=1000x10^4

2) using multiplication of 10 and division by ten with LARS:
100x10^5
100x10=1000 and (10^5)/10=10^4
=1000x10^4

3) using LARS the opposite way: LS RA
100x10^5
=10x10^6

4) using it the opposite way by dividing by 10 and multiplying by 10:
100x10^5
100/10=10, (10^5)x10=10^6
=10x10^6

it doesn't matter what way you choose to do it, but the important thing to notice is that they all equal the same number. all you are doing is manipulating the numbers so that the expnonents are easier to work with when multiplying, dividing, etc. just practice you will get the hang of it in no time.

ofcourse you can do LARS x2, 3, 4, etc.
ex: 100x10^5
if you move the decimal spot to the right TWO places on the left side ('left add') you must subtract TWO from the exponent ('right subtract')
=10000x10^3
 
It all makes sense. Thanks for the refresher course. Its amazing the things you forget when you don't use them anymore.
 
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