> the scale function effect of 0.001 defeated me for years. how can it be 1/1000th, when 1000 has THREE ZEROS

I remember getting tripped up on that all the time. Still do sometimes, having to slow down and "remember" that fewer 0s are needed on the left vs. the right (1000 <-> .001)

I wonder if—back when this notation was "invented"—the decimal or some other mark had been placed above or below the ones place, if this would be easier.

So it would be something like 1000̲ and 0̲001. Now both have the 3 zeros, and it's not optional whether to include the first 0 in the fractional case.

The inverse of 8̲ is 0̲125, the inverse of 50̲ is 0̲02, and half of 5̲ is 2̲5.

The ones place is the only position that doesn't have an inverse position. Tens is tenths, hundreds is hundreths, but one is unity. It's the "pivot point".

I like this idea, and now wonder why the radix point is placed where it is. I assume it has something to do with integers being invented first?

Haha this is painfully relatable. I still never know whether to count the starting 0 in decimals so I get confused reading numbers under 1e-3. Somehow I got a job where I get paid to do math.