So, @robeastaway tweeted, which made me think about zequals.
It's his brilliant time-saving device: when doing arithmetic, forget about all the digits after the first one.
For example, 123 z≈ 100.
You can look at the relative error of zequals compared to doing it precisely

If even the different kinds of digit are too much to keep in your head, you can also do zequals in binary. Here's what that looks like:

But I'm always looking for ways to do worse. So, what if you did zequals, but instead of keeping the most significant digit, you kept the least significant (non-zero) one? I'll call that 'meequals',
For example, 123 m= 300.
What does the relative error of that look like?

It looks like this! The error changes drastically from one number to the next, but you can still see the fractal-ish pattern. That's interesting!
But don't let the scaling on the plot fool you: this method is way, way worse than zequals.