What's the word hidden in the puzzle below?
5102050: (5)(8)  125102050100: (6)(6)(6)  1020501002001000: (5)(5)  5102050100200500: (4)  10002000500010000: (8)(3) 
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The word hidden here is:
NOTES, because this puzzle revolves around denominations of banknotes for commonly traded world currencies.
Look first at the strings of digits comprising solely 0, 1, 2 and 5. These are...
...concatenated numbers, representing (rectangular) banknote denominations of increasing value (hence the title). The name of the currency represented by these banknote values can be worked out with some knowledge, some internet research, and using the numbers in parentheses as a guide to the word lengths involved. Thus we have:
5,10,20,50: (5)(8) = POUND S[T]ERLING
1,2,5,10,20,50,100: (6)(6)(6) = U[N]ITED STATES DOLLAR
10,20,50,100,200,1000: (5)(5) = [S]WISS FRANC
5,10,20,50,100,200,500: (4) = EUR[O]
1000,2000,5000,10000: (8)(3) = JAPAN[E]SE YEN
To get the final answer, we must...
...use the numbers in brackets to help us extract the letters in that numbered position within the names of the currencies (e.g. the 7th letter of 'Pound Sterling' is 't') and read them down the list. I have indicated these target letters in the list in the previous spoiler using square brackets. This gives us five letters (T,N,S,O,E) which we can then anagram to a relevant answer: NOTES. (Much more relevant than TONES or STONE!)