I recall there was a set of "engineering numbers" that were to be used when deciding how big to make something. So that if, for example, you wanted your screw to be 1.36mm you'd instead round up or down to the nearest of these prescribed numbers, perhaps to 1.2 or 1.5. This way everyone's things were more likely to be the same size because instead of randomly selecting sizes that were particular to a specific situation, we'd all be using the same set of pre-selected numbers instead. Does anybody know what this concept was called? Thanks!
You probably mean preferred numbers or any of the other names they go under. There are actually many such series defined in the standards.
It looks like you are talking of the 1-2-5 series in your example.
It is also worth adding that preferred numbers are highly contextual as what numbers are actually sensible will depend a lot on manufacturing processes and existing standards.
For example many standard steel sections, even when nominally metric are actually based on inch sizes so you often see fairly odd mm dimensions on rolled steel sections, simply because it is too much trouble to convert to round metric numbers for no real benefit. Especially for things like structural sections and pipe where new stock needs to be compatible with legacy installations. Similarly BSP is still the norm for gas and hydraulic fittings.
Equally with the rise of international trade most things that need to be standardised are so this is much less of an issue that it once was.
This probably should be a comment really but is a bit too long.