A light year is defined as the total distance that light will move within one year. Light travels about #300,000 \ "km"# per second, so we can use dimensional analysis to figure out roughly how many kilometers does light travel in a year.
#(3*10^5 \ "km")/(color(red)cancelcolor(black)"s")*(60color(red)cancelcolor(black)"s")/(color(red)cancelcolor(black)"min")*(60color(red)cancelcolor(black)"min")/(color(red)cancelcolor(black)"hour")*(24color(red)cancelcolor(black)"hours")/(color(red)cancelcolor(black)"day")*(365color(red)cancelcolor(black)"days")/"year"#
#=9.4608*10^12 \ "km/year"#
#~~9.5*10^12 \ "km/year"#
