First, we predicted which fractions would have a terminating decimals, this was quite easy as we could use process of elimination. 2/3 - this is really easy as it is commonly known that this is equivalent to 0.66 reoccurring. Then, you can eliminate 7/12 as there is no possible way to convert it into any number that ends with zero(10,100 etc.) apart from numbers in the 120 times table.11/14 is also easy to eliminate for the same reason as the last one.8/15 is a harder one than the rest, but we eventually found out that it also wouldn't convert into 10,100 etc., this leaves us with: 4/5, 17/50,3/16 and 5/8. Originally, we thought that 17/50 wouldn't be terminating, but then realised it could be converted into 34/100, this makes it terminating. Thus we shall end our explanation here.
NRICH admins, please accept.