According to Star Trek, Warp 8 is 8 times the speed of light. If the star ship Voyager can travel at Warp 8, how many miles can it travel in a year? Write your final answer in scientific notation and show at least one step of your work.

- anonymous

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- anonymous

what is the speed of light?

- anonymous

google it if you don't know and post it here.

- anonymous

ttully, are you interested in the answer or not? I need your feedback to help you.

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## More answers

- anonymous

yes i will google it

- anonymous

the speed of light = 299 792 458 m / s

- anonymous

okay. to make matters simple, we generally assume the speed of light to be 300000000 m/s or 3X10^8 m/s
so, what is Warp 8 then? What is that speed equal to?

- anonymous

just tell me what Warp 8 means. Unless you don't want the answer. In that case I won't waste your time or mine.

- anonymous

I dont know what warp 8 means

- anonymous

it is given in the first sentence of the problem. read it.

- anonymous

8 times the speed of light

- anonymous

8 X 299 792 458

- anonymous

you must always say what that number means. 8 X 299 792 458 could mean feet, or pounds or number of fish you caught last year. what is it?

- anonymous

8warp X 299792458m/s

- anonymous

no, you should say Warp 8 = 8 X 299792458m/s

- anonymous

okay. so we have the speed. now, what is the distance traveled in a year?
the formula for distance is speed X time.
so how much time is one year?

- anonymous

2398339664m/s

- anonymous

okay, that is the speed. now, what is the time?

- anonymous

not sure

- anonymous

okay. how long is a year?

- anonymous

12 months

- anonymous

okay. and how many days in each year?

- anonymous

360

- anonymous

really? when was the last time you had 360 days in a year. A year has 365 days. Look it up.

- anonymous

anyway, how many hours in a day?

- anonymous

24

- anonymous

and how many seconds in an hour?

- anonymous

60

- anonymous

are you sure? 1 hour is 60 seconds long?

- anonymous

60min

- anonymous

right, and each minute has how many seconds?

- anonymous

60

- anonymous

okay. so a minute has 60 seconds. and hour has 60 minutes, a day has 24 hours. a year has 365 days.
so the total number of seconds in a year is 60 X 60 X 24 X 365

- anonymous

so give me the number of seconds in a year. Multiply all that using your calculator.

- anonymous

31536000

- anonymous

okay good. so if you are traveling at warp 8 it means that you travel 2398339664 meters each second. so how much distance would you travel in 31536000 seconds?

- anonymous

7.563403964

- anonymous

oh. you travel 7.563403964? what is that? is it 7.5 feet? or 7.5 kilometers, or 7.5 pounds of meat? or 7.5 chips?

- anonymous

miles

- anonymous

so your answer is 7.5 miles?

- anonymous

no it is 7.5miles X 10 to the 9th power

- anonymous

is that right? and how did you get that answer?

- anonymous

I dont know if that rigt or not. But I mad the 7.563403964 into scientifice notation

- anonymous

well, if I told you I travel 1 foot every second, how much distance will I cover in 10 seconds?

- anonymous

10ft

- anonymous

why not 10 miles?

- anonymous

because you said 1ft a second

- anonymous

right. if you travel at warp 8 speed it means you travel 2398339664 METERS each second, how much distance would you cover in 31536000 seconds. Why did you say 7.5 X 10 ^9 MILES?

- anonymous

how come you changed meters to miles?

- anonymous

because it has to be in scietifice notation

- anonymous

what did you think scientific notation means?

- anonymous

its so you dont have to use so many numbers

- anonymous

actually, don't worry about the scientific notation now. just tell me how many METERS it travels in one year.

- anonymous

7.7m

- anonymous

7.5meters

- anonymous

are you sure? it travels just 7.5 meters in one whole year?

- anonymous

no im consfused now

- anonymous

if my speed is 10 meters per second, how many meters would I travel in 10 seconds?

- anonymous

are you familiar with meters? it is just a measure of distance. One meter is roughly equal to one yard. so don't get confused by the word 'meter'

- anonymous

yes

- anonymous

so answer my question: if my speed is 10 meters per second, how many meters would I travel in 10 seconds?

- anonymous

10

- anonymous

wrong. do you know how distance is calculated? distance is speed X time

- anonymous

so if my speed is 10m/s, how much distance would I cover in 10 seconds?

- anonymous

100

- anonymous

100 what? feet, seconds, pies?

- anonymous

meter

- anonymous

okay. so if my speed is 10 m/s, I travel 100 meters in 10 seconds.
Using the same logic,
if my speed is 2398339664 m/s , how many meters do I travel in 31536000 seconds?

- anonymous

7.563403964E16

- anonymous

okay. so 7.563403964E16 meters is the answer. That is also the scientific notation.
Scientific notation simply means you take a number, say 123455 and express it as 1.23455 X 10^5.
so the answer in your case is 7.563403964E16 which can also be written as 7.563403964 X 10^16

- anonymous

all in meters.

- anonymous

The letter E in the answer means you multiply the number before E with 10^ the number after E
so 7.563403964E16 means 7.563403964 multiplied by 10^16.
so your answer in scientific notation is 7.563403964E16 meters or 7.563403964 X 10^16 meters.

- anonymous

http://www.chem.tamu.edu/class/fyp/mathrev/mr-scnot.html
http://en.wikipedia.org/wiki/Scientific_notation
scientific notation is just a way to represent NUMBERS. It does not mean that you should change meters to miles or anything like that.

- anonymous

ok thank you

- anonymous

you are welcome. note that E means the exponent. it doesn't always have to be 10.

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