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Edit

I misread the OP's question and didn't realize he was looking for an historical event. I apologize. This isn't an answer to his question. But I had a lot of fun writing it, so I'm going to leave it up. Please don't vote for it. Cheers.

Not that I can believe (as an American)

In reality, the issue is cost. It's the consequence of a capitalistic society combined with a representative government.

Senator: We need to stop using multiple systems of measurement!

People: OK, we can see the value in that...

Senator: It means changing our schools and businesses! Everything from the paper we use to the measuring cups in our kitchen drawers! Think of the jobs! Think of the opportunity!

People: Wait, my measuring cups? Do you even know what dry measure is in the metric system? My paper? Who's going to pay for all this?

Senator: We'll need to pass a temporary tax to help subsidize business and schools to affect the change!

People: There hasn't been a temporary tax in U.S. history!1 I'm not voting for that! Government hasn't used a dollar efficiently since day one! Heck no, we won't go!

And after the protests have died down, we're back at square one.

We've had the same problem with adopting credit card security measures in use in Europe for years and years — the cost to convert everybody is whomping enormous, no one's willing to pay the price, and no one's willing to vote for anybody who's willing to committ to deficit spending to make it happen. The credit card industry finally forced the issue by making businesses responsible for fraudulent spending if they didn't change — and two years later there are a lot of businesses that still haven't changed.

Has there ever been examples of this happening successfully? Oddly, there are (kinda). The Feds outlawed the manufacture (and eventual sale) of 40W, 60W, 75W, and 100W incandescent light bulbs (a lovely attempt by the environmentalists to force the citizenry to reduce their power bills. You'd be surprised what we fight against). It happened — and while some people cheered, many loathed it.

It also happened with the conversion of TV broadcasting from analog to digital. The only way it happened was by the Feds giving away free analog-to-digital conversion boxes.

But converting the way we measure things?

In the end, people don't care about light bulbs so long as they fit in the lamp and do their job. Kinda ditto with TV. You don't actually need to think about anything (and Americans as a people aren't the best thinkers, not since WWII anyway). On the other hand, swaping out all our rulers, scales, forcing us to think about carrots in terms of grams.... (Although it has worked for soda. That's a curiosity all by itself....)

So, despite our entire scientific community using SI units, and pretty much all our cars using metric nuts and bolts, I honestly can't see any way to force such a change on the people other than the government simply choosing to do it — and whichever political party is in power at that time can expect to loose the presidency for 8-16 years because people will absolutely howl. Suddenly all of their great-grandma's recipies don't work anymore.

Unless...

Unless the government simply chose to mandate that all labeling of all products had to be metric-only. After that it would take (literally) 100 years to get everyone on board, but it would eventually happen. I think. (Oh, people would howl.)

Yeah. We're funny people.