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how can you put (7.7×108)×(4.9×10−5) as a scientific notation.

Guest Jun 2, 2017
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 #1
avatar+1224 
+1

First evaluate the given expression and then put into scientific notation:

 

\(\textbf{(7.7*108)}*(4.9*10-5)\) Do \(7.7*108\)first because it is in parentheses.
\(821.6*(\textbf{4.9*10-5})\) Do what is in parentheses first before evaluating anything else
\(\textbf{821.6*44}\) Finally, simplify \(821.6*44\)
\(36150.4\)  
   

 

Of course, we aren't done yet! We have to convert this number into scientific notation. Let's do it:

 

\(3_\leftarrow6_\leftarrow1_\leftarrow5_\leftarrow0.4\) As shown, move the decimal to the left or right until you get a number between 1 and 10
\(3.61504\) Now, you must figure out how many lots of 10's you need to multiply by to return to the original answer. If you moved the decimal place to the right 4 times, then you divided the number by 10^4. You must reverse this change. The reverse of division is multiplication. Therefore, multiply this number by 10^4 and you're done!
\(3.61504*10^4\) This is your final answer in scientific notation!
   
TheXSquaredFactor  Jun 2, 2017
 #2
avatar+90618 
+1

 

how can you put (7.7×108)×(4.9×10−5) as a scientific notation.

Thanks X squared, yours is a good answer too :))

 

I think you mean  (7.7×10^8)×(4.9×10^−5)

You use the ^ (calleded a hat, or more correctly still a caret) to indicate a power.

 

\( (7.7×10^8)×(4.9×10^{−5})\\ =7.7\times 4.9 \times 10^{8+-5}\\ =7.7\times 4.9 \times 10^{8+-5}\\ =37.73 \times 10^{3}\\ =3.773 \times 10^1 \times 10^{3}\\ =3.773 \times 10^4 \)

Melody  Jun 2, 2017

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