So I've been reading up on non-decimal currencies and was wondering why they were invented. Was this because mathematics wasn't advanced enough to create a decimal system or did it have something to do with how the coins' value was construed (i/e as a fraction of set amount of silver or gold?).
For the same reason other units of measurement were non-decimal: Using the technology of the time it was easier and more intuitive to divide things into halves and quarters than into tenths.
That precious metals were used was certainly part of it also, as you would encounter similar measurement issues dividing a lump of silver as you would a grain harvest. Spanish dollars were literally cut up into parts ("pieces of eight"), which is easiest to do fairly into powers of two -- consider folding a piece of paper in half and inspecting the fold.
The US system is actually a hybrid of decimal and binary. The Coinage Act of 1792 started with
Half-cents and cents
Half-dimes and dimes
Quarter dollars, half dollars and dollars
Quarter eagles, half eagles and eagles (one eagle = $10). Yes, there were coins worth $2.50, until 1929.
Each unit was worth 10x the lower unit, but was itself divided with powers of two.
This is not only why we call them "quarters", but also why they have "quarter dollar" inscribed on them rather than "one quarter" or even "25 cents" -- they've always said "quarter dollar".
Modern "nickels" were considered a separate coin when they were introduced, as the half-dimes were made with half the silver of the dime, but the nickels had no silver and were a different size (larger).
Anyway, as the needs of commerce grew, including modern accounting methods, the advantages of calculating in base 10 became obvious.