[jrowen]

On the other hand, it's completely unintuitive that "Sun Protection Factor 30 = 1/30th of UV light passes through it", and I had no idea there was any correlation before this comment.

The only intuitive bit about that system is "bigger number does more." I feel like I would have more readily understood it if it just said "blocks 97% (or 98%) of UV light" instead of numbers I assumed were somewhat arbitrary.

[parineum]

The intuitive part comes when comparing two options.

If you use 20 instead of 10, you'll be exposed to half as much UV even though it's only an additional 5% of protection.

The number could just be the percentage of exposure (5 v 10) and express the same relationship but the denominator has the advantage of bigger numbers being more protective while still being more intuitively comparable.

Many people would see 90% vs 95% and not intuit that it's twice the protection.

[jrowen]

I'll grant that it's complicated, as the comments on this post have demonstrated.

But half the exposure isn't quite equivalent to twice the protection.

All my life I just thought they were somewhat arbitrary numbers, I didn't correlate them to any actual measurable quantity, and I would assume it's the same for most people. So while I would agree that that representation "gets the job done," I don't think it contributes to a deeper understanding.

I do feel like if you saw "90%, 95%, 97%, and 98%" on the shelf it would start to make some kind of sense, and then when people talk about it ("what's the difference between 97 and 98?") the underlying concept would become more apparent. Using a kind of converted magic number scale that doesn't work like other things seems unhelpful, but I'm certainly not an expert nor the intended audience.