Loose ends: scientific notation

Remember how I said that you could increase the shift counter by shifting right, and decrease it by shifting left? Remember how I also said that shifting left was the same thing as multiplying by ten? So if we had a number at eight shifts, isn't shifting left eight times (to get back the original number) the same as multiplying by ten eight times?

The answer is yes, and in fact this leads us to the common mathematical way to express these shifts. Let's say we have the number 23 at eight shifts, which means that the actual number we're representing is a 23 with eight zeros, or 2 300 000 000. But since each left shift is the same as multiplying by ten, we can also write this number as 23 · 10 · 10 · 10 · 10 · 10 · 10 · 10 · 10.

Now, there's a common mathematical notation for writing a number that's multiplied by itself a few times, like this: 2 · 2 · 2 = 2³. In the same way, we can also express that sequence of eight tens like so: 10⁸, and we can write the whole number like so: 23 · 10⁸. This way of writing numbers is called "scientific notation", and the little ⁸ after the 10 is called "exponent". Note that this exponent is exactly the same number as our shift counter (see also: terminology).