Question

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

Answer 1

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.