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# math

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A spaceship traveled at a speed of 5,000 miles per hour for 30,000 hours.

How many miles, written in scientific notation, did this spaceship travel?

Guest Dec 15, 2017

#2
+2190
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I would convert both the multiplicand and multiplier to scientific notation and then multiply.

$$5000\Rightarrow5*10^3\\ 30000\Rightarrow3*10^4$$

Now, multiply them together.

 $$\left(\textcolor{red}{5}*\textcolor{blue}{10^3}\right)\left(\textcolor{red}{3}*\textcolor{blue}{10^4}\right)$$ Multiply these together. The numbers in red and blue can be combined together. The blue numbers can be multiplied because they both have identical bases. $$15*10^{7}$$ Of course, we must remain proper with scientific notation rules. This means that the beginning number must be bounded between 1 and 10. $$1.5 ×10^8$$ I find that the traditional multiplication symbol is used with scientific notation, so I used that particular symbol; however, it is not required.
TheXSquaredFactor  Dec 18, 2017
#1
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5,000 x 30,000 =1.5 x 10^8 Miles.

Guest Dec 15, 2017
#2
+2190
+2

I would convert both the multiplicand and multiplier to scientific notation and then multiply.

$$5000\Rightarrow5*10^3\\ 30000\Rightarrow3*10^4$$

Now, multiply them together.

 $$\left(\textcolor{red}{5}*\textcolor{blue}{10^3}\right)\left(\textcolor{red}{3}*\textcolor{blue}{10^4}\right)$$ Multiply these together. The numbers in red and blue can be combined together. The blue numbers can be multiplied because they both have identical bases. $$15*10^{7}$$ Of course, we must remain proper with scientific notation rules. This means that the beginning number must be bounded between 1 and 10. $$1.5 ×10^8$$ I find that the traditional multiplication symbol is used with scientific notation, so I used that particular symbol; however, it is not required.
TheXSquaredFactor  Dec 18, 2017