SOLUTION: One light-year is defined by astronomers to be the distance that a beam of light will travel in 1 year (365 days). If the speed of light is 186,000 miles per second, how many miles

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Question 1208144: One light-year is defined by astronomers to be the distance that a beam of light will travel in 1 year (365 days). If the speed of light is 186,000 miles per second, how many miles are in a light-year? Express your answer in scientific notation.
Found 3 solutions by josgarithmetic, ikleyn, math_tutor2020:
Answer by josgarithmetic(39614)   (Show Source):
You can put this solution on YOUR website!
You should be able to identify the necessary conversion factors. The other question and setup shown there should be very helpful.

You should find expression , and then you still need to put into scientific notation, compute, and adjust.

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1 year---------------How many miles?

You should on your own, be able to find:
How many days in a year;
how many hours in a day;
how many minutes in an hour;
how many seconds in an hour.

Answer by ikleyn(52756)   (Show Source):
You can put this solution on YOUR website!
.

This problem was posted to the forum and answered about a month ago.

See the solution and the answer to this question by tutor ankor@dixie-net.com at this forum under the link

https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1207558.html

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To learn more about determining speed of light, read these fascinating sources

(1) Who, when and how first determined speed of light

https://www.amnh.org/learn-teach/curriculum-collections/cosmic-horizons-book/ole-roemer-speed-of-light#:~:text=In%201676%2C%20the%20Danish%20astronomer,eclipses%20of%20Jupiter's%20moon%20Io.

(2) The book by Michelson about his experiments on determining speed of light

https://www.gutenberg.org/cache/epub/11753/pg11753-images.html

https://apps.dtic.mil/sti/tr/pdf/ADA434600.pdf

Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!

Answer: 5.87 * 10^12 miles
In word form this is 5.87 trillion miles.
This value is approximate.

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Explanation

Think of "186,000 miles per second" as

Then multiply that fraction with these 4 extra conversion factors

Each conversion factor is based on these facts
60 sec = 1 min
60 min = 1 hour
24 hours = 1 day
365 days = 1 year (ignoring leap years)

Notice very carefully how I've set up the units so that nearly everything cancels out.

The only thing left will be "miles" up top and "years" down below.

=

=

=

I'm rounding to 3 significant figures since the "186,000" value is also to 3 significant figures. Those zeros aren't significant.

The "times 10^12" portion represents "trillion" which means is the same as saying "5.87 trillion".

Light travels roughly 5.87 trillion miles in one year.
Therefore we conclude there are roughly 5.87 trillion miles in a light-year.

When rounding to 1 significant figure, it yields roughly 6 trillion miles in a light-year.
Which matches with this source
https://spaceplace.nasa.gov/light-year/en/
Quote from the page: "One light-year is about 6 trillion miles (9 trillion km). That is a 6 with 12 zeros behind it!"

Further confirmation
https://www.wolframalpha.com/input?i=1+lightyear+to+miles
The result from that page is roughly 5.879 trillion miles.
There is rounding error in our scratch work above because the "186,000" value is an approximation (instead the speed of light is actually closer to 186,282 miles per second; this value is also an approximation)
Regardless of the rounding error, we get in the same ballpark at least.