I can think of two significant interesting systemic or emergent human behaviors that are the result of using numeric math for valuation: the process of comparing, estimating, and communicating value relative to an external system.
The value of currency will always be relative to some commodity
Decimal and non-decimal currency have different functions of incentive (similar to coins, paper, and plastic)
Because currency will always try to be uniform in value we have a tendency to prefer some numbers over others (you think $20 is almost no money but $40 seems like 3x the amount). But in reality the value of money is trying to be uniform and consistent. Any first grader can tell you that $40 is twice as much as $20 but we still have preferences to exaggerate the linear relationship into one that is more logarithmic.
At the same time we imagine billions of dollars as being only a few hundred more than a million dollars and so we undervaluate the number of money at the other end of the spectrum.
Because currency is relative to a commodity when we start learning about currency and how to count it we think of something that is important to us and we estimate how many of those things we could buy in order to understand the value that is hidden behind a number.
When we go to another country we look up how the currency is valued compared to the currency that we grew up with. (How many Singaporean dollars is one US dollar?) Then often people will calculate in their head (oh okay 3 SGD is about 2 USD). This strategy works well for a while but eventually your brain will automatically accept the SGD for what it is and you will know the “acceptable price” for things that you often buy.
Perhaps a better strategy is to ignore your home currency completely and “learn currency” again. Skip the currency conversion and just think about how many LEGO sets or how many McWhoppers you can buy. But then you might spend too much money or maybe even too little.
Non-decimal currency is very interesting. Sellers feel more free to sell their products at prices between prices. The Philippine Peso is a good subject for this analysis. With Singaporean dollar a lot of sellers will only sell at increments of S$1.00 but there are at least 10 prices that are possible within S$1.00. With the Philippine Peso there is pretty much no restriction on price fractionality despite being a non-decimal currency.
Buyers and sellers sell at prices which would be considered weird outside of Walmart (think $2.63): the bus is 9 PHP. A meal could be 50 PHP, 70 PHP, 75 PHP, 230 PHP or any price in between and it wouldn't feel weird or awkward. Well I guess with numbers that are rounded to 5 but still that's like 20x the number of acceptable sounding prices to the Singaporean dollar. (Tax is usually included in the display price in both Singapore and the Philippines. The previous paragraph might make less sense if you're thinking about post-tax US restaurant prices--because post-tax US prices are always weird prices.)
The barter system did not have these interesting behaviors because valuation was almost always done locally. Of course, there was still an established hierarchy of value (iron > gold > silver…) but artifacts before the concept of mass-production were usually handmade with variation such to catch the eye of the buyer (beauty is in the eye of the beholder).