# Why is the speed of light rounded to 286 Mm in calculations involving frequencies below 30MHz?

I understand that in order to make the maths simpler, frequency ($f$) is expressed in megahertz (MHz) and the velocity of propagation in free space ($c$) for frequencies above 30 MHz is expressed as and rounded to 300 megameters/second (Mm/s). The actual speed of light is 299,792,458 meters/second, so expressing and rounding this to 300 Mm makes sense.

I'm confused why it is rounded to 286 Mm when $f < 30\ \mathrm{MHz}$. Please explain. An excellent answer will show the maths.

• @KevinReid actually that is how I originally had all of mine but it was recommended to me that I subscript them.
– Dan
Commented Oct 29, 2013 at 18:33
• That's surprising. Could the recommender perhaps provide a citation for that style? Commented Oct 29, 2013 at 19:57
• @KevinReid this was the recommendation
– Dan
Commented Oct 29, 2013 at 21:18
• Ah, I see. That recommendation was referring to writing $f_{\mathrm{MHz}}$ instead of $f\ \mathrm{MHz}$, because the latter means $f$ multiplied by MHz which is wrong because variables for quantities are generally assumed to already have their proper units/dimensions, and the subscript is just a hint about what units the numeric value should be in. That's different from a constant, where you really do want to say $30$ multiplied by $\mathrm{MHz}$, or $30\ \mathrm{MHz}$. Commented Oct 29, 2013 at 22:15

$$\lambda_{\mathrm{m}} = \frac{(300\ \mathrm{Mm})(0.95\overline{3})}{f_{\mathrm{MHz}}} = \frac{286\ \mathrm{Mm}}{f_{\mathrm{MHz}}}$$