I taught an hour-long class at work where I'd prepped an example to warm the group up, which involved converting the sales material for a US car that got 26 mpg to a Canadian market using liters per 100 km. 26 mpg is carefully chosen because between 1/3 and 2/3 (usually on the lower end) would get it right (~9 liters per 100km) and the others would often come up with around 11 (km per liter).
I could then ask "who got a figure around 9?" and "who got a figure around 11?" and both groups would raise their hand feeling pretty confident they'd gotten it right. I'd then introduce and walk them through dimensional analysis and finish with an example that was more complex and error-prone, but was pretty straightforward if you just applied DA.
(The main point of the class was "use correct units" rather than "learn dimensional analysis".)
The great thing about that conversion is that due to the reciprocal relationship the same conversion formula works both ways, so you don't have the risk of converting the wrong way.
I could then ask "who got a figure around 9?" and "who got a figure around 11?" and both groups would raise their hand feeling pretty confident they'd gotten it right. I'd then introduce and walk them through dimensional analysis and finish with an example that was more complex and error-prone, but was pretty straightforward if you just applied DA.
(The main point of the class was "use correct units" rather than "learn dimensional analysis".)