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system, income, increase, profit, business, use, sense, etc.

So many nouns are hard for me to determine whether they are countable, uncountable, or both in some cases.

I have to look up each new word in the dictionary every time, which consumes most of my writing time.

Q1. Whenever Americans learn a new word, do they try to look it up in a dictionary to find whether it is countable or not?

If they don't, do they just depend on common sense for such determination, which is likely to cause frequent errorneous uses and spread-out of errors, which Americans are willing to tolerate? If they do tolerate it, I feel I don't have to look it up in a dictionary. ;-)

Q2. Or are there better knacks to determine a word's countability non-native speakers can learn?

I know material nouns, and abstract nouns are uncountable, which definitely is not enough to determine a noun's countability.
Comments 
zazzexWhenever Americans learn a new word, do they try to look it up in a dictionary to find whether it is countable or not?
I don't know if this will be of any help but, for what it's worth, here goes.

Whenever I encounter a new word (one that I have to look up) I'm never thinking in terms of countable/uncountable. I'm just looking for the definition. Once I have that I know everything I need to know to use the word myself. The concept of countable/uncountable isn't something that native speakers ever explicitly think about (except in special circumstances, such as these forums). In fact, until I started reading and posting here, I had never encountered the idea of 'countable/uncountable' as it relates to nouns, it's just something native speakers absorb as part of the language.

Well, as I said, I don't know how much this helps, or if it helps at all, but it's the best I can do.
Hi,

I woneder if you are thinking a bit of the terms 'countable/uncountable' as labels, without thinking enough about what they actually mean.

A countable noun is something you can actually count.

eg '1 chair, two chairs, 3 chairs'.

eg '1 mistake, 2 mistakes, 3 mistakes'.

I can understand why you might have trouble with some of the words in your list of examples, but not all of them.

eg There are many systems in the world. Is it really hard for you to see that you can count them?

Best wishes, Clive