How do you use scientific notation to express a lightyear in miles?

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Answer 1 · 2015-03-25T11:28:14

I'll do it in meters - you can convert this yourself.

Speed of light #c=299792458 m//s# or in scientific notation:
#c=2.99792458*10^8m//s#
We may round that to #2.998*10^8#

Multiply by
#3600=3.6*10^3# (seconds in an hour)
#24=2.4*10^1#(hours in a day)
#365.25=3.6525*10^2# (days in a year)

On your calculator you do this like:
#2.998*3.6*2.4*3.6525=94.61=9.461*10^1#

Now add all the other exponents to this final (#1#) exponent
#8+3+1+2+1=15#

So the final answer #Ly=9.461*10^15# meter
(just to make sure I checked with Wikipedia, and it checks)

It should be easy to do the same with miles
(your answer should be #~~5.9*10^12# miles.