The First Excited State takes on approximations with Assume a spherical physicist

Everybody who’s taken any sort of math class knows that a statement like N+1 = N is simply ridiculous. Everyone, that is, except for the physicist. Let’s say that N is a really huge number, like if someone dumped an entire truckload of M&M’s in your driveway. If you turned your back on me to watch the truck drive away, and I threw another M&M in the pile while you weren’t looking, would you really notice? What if I snuck one while you were looking to the sky to thank God for this miracle? No, you’d really have no idea. So in this case, for all practical purposes, N+1 = N-1 = N. We make this approximation all the time in my statistical mechanics class, where N represents some astronomically huge number, like the number of water molecules in your glass.

There’s also the trick of rounding numbers to 1, 2 or 5 in order to get an approximation when a calculator isn’t handy. You can usually get within a factor of 2 and perhaps better, depending on how crudely you round things.