From the definition of velocity,
Thus by ratio and proportion, if one wavelength is 600nm, then
The idea here is that you need to consider the speed of light constant and use its known value to calculate how many wavelengths would fit per meter of distance traveled.
As you know, the speed of light can be approximated to be equal to
Now, a nanometer, or
The conversion factor between these two units will thus be
#"1 m" = 10^9"nm"#
At this point, a unit conversion will take you from meters to nanometers
#3 * 10^8 color(red)(cancel(color(black)("m"))) * (10^9 "nm")/(1color(red)(cancel(color(black)("m")))) = 3 * 10^(17)"nm"#
Since one wavelength covers
#3 * 10^(17) color(red)(cancel(color(black)("nm"))) * "1 wavelength"/(6 * 10^2color(red)(cancel(color(black)("nm")))) = color(green)(5 * 10^(14)"wavelengths")#
The answer is rounded to one sig fig, the number of sig figs you have for the wavelength of the emitted light.