[parsifal]

LOL! But seriously, 186,000 x 186,000 = a really big number. How do we accurately measure the output number? After all, everything close is blown to hell and back. How do know that E doesn't really = m x 185,000^2???, or 187,000^2. (Those are really big numbers, too.)Sign me, parsifal the curious?

[Doctor Stochastic]

One weighs (indirectly) the mass of various atoms. Then one measures the energy given off by alpha or beta decay leading to the transmutation of one type of atom to another. Plug in the speed of light and there's the answer.

[Physicist]

LOL! But seriously, 186,000 x 186,000 = a really big number. How do we accurately measure the output number? After all, everything close is blown to hell and back. How do know that E doesn't really = m x 185,000^2???, or 187,000^2. (Those are really big numbers, too.)Sign me, parsifal the curious?

Don't be spooked by the size of the number. The accuracy is determined by the number of significant digits you carry; the decimal places are just along for the ride. (I take it you've never used a slide rule.)

And after all, "186,000 miles per second" is really just a choice of units. When I do calculations for work, the speed of light = 1, and is unitless. All you have to do is measure time in the same units you use to measure length. If you set h-bar = 1, you can measure everything in units of energy (or inverse units of energy). The unit choice c = h-bar = 1 is often referred to as "God's units". Time and space are conveniently measured in units of GeV^-1.