Invaluable intuitively seems to imply a higher degree of importance.
Please explain the difference between valuable and invaluable and in what context you'd use one or the other.
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Technically, invaluable works like priceless. They mean that something is of a value which cannot be expressed in numbers. For example great memories, happiness, health, or whatever else you prefer. They are invaluable, because they cannot be sold or bought. They have no price.
On the other hand, valuable means something is of a high value, which can be expressed in numbers. Like a golden ring. It's valuable, because it costs $1000.
In COCA, valuable appears much more than invaluable, and it is more common in academic writing (where it might be expected as a formal-sounding synonym for good, important, worthwhile, things we need), whereas it is less common in speech. (The speech examples in COCA are from news broadcasters so they may not fully represent unscripted speech.)
From most to least frequent use of valuable, here are some examples of how it's used. In academic writing, it almost exclusively has the more figurative meaning of important; in other places, it sometimes refers to the high monetary value of real goods.
[Acad] modern collections management systems will provide easy access to valuable additional data [Acad] foreign-born faculty members make valuable contributions to the research mission
[Mag] There's a vast supply of valuable metal in Alaska
[Mag] such genetic information will provide valuable insights into issues
[News] thieves who steal copper, brass, bronze and other valuable industrial metals
[News] If you are judging who is the most valuable player then I think Wondo has a great shot
[Fic] A valuable piece of pink jade of that size and perfection
[Fic] from a merchant who was buying a small but valuable patch of groznium-rich soil
[Spok] we're running short of a lot of valuable resources, and we don't have that much zinc
[Spok] There's some really valuable tips there, so I would encourage people to take a look
Invaluable, in COCA, occurs less than valuable, but follows the same pattern of being used more in academic writing, then magazines, news, fiction and finally least in speech. However, I could not find any instances where it clearly refers to real monetary value. Even when a reference to money is made, the meaning is more like very important, so that people say coupon books and funds are invaluable. For example:
[Acad] Finally, the authors acknowledge the invaluable contributions to the project
[Mag] ferns are invaluable for a reliable, low-maintenance understory
[News] These funds were invaluable in giving cash-strapped farmers a chance to remain
[Fic] the gray kitty is Pewter, Market's invaluable assistant, though she's often over here
[Spok] His leadership has also been invaluable in helping our country