How can you easily compute in your head 84.4084% of 25?
All the non-zero digits in 84.4084 are divisible by 4.
From there you can do the following steps in one go easily:
Divide 84.4084 by 100 to get the raw decimal form, then multiply by 25 to get the answer (i.e. 84.4084 * 1/100 * 25). But this is the same as multiplying 84.4084 by 25/100 (= 1/4), which is the same as dividing by 4. And since all the non-zero digits of 84.4084 are divisible by four, we can trivially compute the answer: 21.1021
Well, not sure if this is easy enough, but
multiplying 84.4084 by 5 two times is definitely doable in the head (however, I only managed to do that from the second attempt). $84 \cdot 5 = 420$, $844 \cdot 5 = 4220 \implies 84.4084 \cdot 5 = 422.042$. In a similar way we get $422.042 \cdot 5 = 2110.21$. The answer is therefore $21.1021$.