SOLUTION: 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?

Question 1137969: 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?
Found 3 solutions by Boreal, Theo, josgarithmetic:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
5 * 10^3* 3*10^4=15*10^7 which is 1.5 * 10^8 miles
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
5000 = 5 * 10^3.

30,000 = 3 * 10^4.

5000 * 30,000 is therefore equal to 5 * 10^3 * 3 * 10^4.

this is equal to (5 * 3) * (10^3 * 10^4) which is equal to 15 * 10^7.

if you divide 15 by 10 and multiply 10^7 by 10, the result is the same number because you are dividing by 10 and multiplying by 10 which is equivalent to multiplying which keeps the same value as before.

therefore 15 * 10^7 is equal to 15/10 * 10^7 * 10 which is equal to 1.5 * 10^8.

that's how far the spaceship traveled in scientific notation.

1.5 * 10^8 is equivalent to 1.5 * 10^2 * 10^6 which is equivalent to 1.5 * 100 * 1 million which is equal to 150 million miles.

with big numbers such as this, it's much easier to use scientific notation.

you could also have used some logic to get to the same conclusion because these numebrs aren't that big that doing it another way is out of the question.

for example,

5000 * 30,000 is equal to 5 * 1000 * 30 * 1000 which is equal to 150 * 1000000 which is equal to 150 million.

150 million is equal to 150 * 10^6.

divide 150 by 100 and multiply 10^6 by 100 and you get 1.5 * 10^8 which is the same value as 150 million.

here's a reference on scientific notation.

https://www.mathsisfun.com/numbers/scientific-notation.html

here's another reference that also contains problems and solutions.

http://lasp.colorado.edu/~bagenal/MATH/math1.html

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
duplicate from two or three days ago
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