The most common example of finding percentage of would be discounts. If something cost $510, a discount of 30% would be $153. Usually, we would divide 30 by 100 and multiply by $510 to get $153.
I gained a new perspective during one of my lessons, when I realised that my student was actually breaking the problem down to more manageable steps. This student first divided $510 by 10 to find what is 10% of $510, which is easily found to be $51, by moving the decimal point. Next, to get 30%, all that is required is to multiply $51 by 3, which gives $153.
Amazing from my point of view. A new way to solving problems involving % of. With single digit % like 7%, 1% of $510 is found first. Again, moving the decimal point to get $5.10 before multiplying by 7 to get $35.70.