What is a light-year, mathematically?
•1 light-year  =     c ´ t    (where c is the speed of light and t is one year)

= 3.0 ´ 108 m/s    ´   365 days
= 1.1 ´ 1011    (m ´ days /s)
•but we know light-years is a distance and must have “dimensions” of distance.  We should have units of just meters.  The fact that we have this extra (days/s) means we have left something out.
•If we multiply by  (24 hr/day ´ 60 min/hr ´  60 sec/min) the units will work out right and so will the numerical answer
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•
     
•       = 1.1 ´ 1011 ´ 24 ´ 60 ´ 60  m
       = 9.5 ´ 1015    m
       = 9.5 ´ 1012 km
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