SOLUTION: I have freshman algebra, and I had an assignment today with scientific notation the problem was (3,000)^3. When solving the problem I multiplied 3,000 x 3,000 x 30000= 270,000

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Question 235108: I have freshman algebra, and I had an assignment today with scientific notation
the problem was
(3,000)^3. When solving the problem I multiplied 3,000 x 3,000 x 30000= 270,000.00. I wrote the scientic notation as 2.7 x 10^9 was I correct
Found 2 solutions by solver91311, Edwin McCravy:
Answer by solver91311(5072) About Me  (Show Source):
You can put this solution on YOUR website!


In the first place 270,000.00 is not correct.

3000 times 3000 times 3000 is 27,000,000,000. The three 3s give you the 27 and the nine zeros give you nine zeros.

Then you wrote , so work backwards from your answer to check if that is correct.

Start with 2.7 and then move the decimal point 9 places to the right:

2,700,000,000. Compare that to 27,000,000,000. Ten times too small. So what you need is: .

You were off because 3 cubed is 27, but you are writing 2.7

John

Answer by Edwin McCravy(2920) About Me  (Show Source):
You can put this solution on YOUR website!
THAT'S NOT THE WAY YOU'RE SUPPOSED TO DO IT! 


solver91311 showed you how to do it the way you were
trying it. You can indeed get the answer the way you're 
trying and the way solver91311 showed you, if you don't 
make a mistake.  But you aren't supposed to do it that
way!  Here's the way you're supposed to do it:



Write  as 



Consider  as 



Remove the parentheses by multiplying
the two inner exponents by the outer exponent:



Do the actual multiplying:



Since , replace  by 



But that is not scientific notation because
 is greater than , and the first part
of scientific notation must be between  and , inclusive
of 1 but exclusive of .  So write  in scientific
notation as :



Add the exponents of 10



Do the actual addition:



Edwin