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In referring to the grouping of units, tens, hundreds of simple units and units, ten, hundreds of thousands, etc., what is the correct word to use? Does the term "hierarchy" have any definite use within the decimal system?

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Could you clarify your question as to what you mean by "hierarchy"? Certainly so, in terms of magnitude:

What you seem to be describing is that in the decimal system

  • a unit is represented by $10^0$,
  • ten units as $= 10\cdot 10^0 = 10^1 = 10$,
  • a hundred units $=100\cdot 10^0 = 10\cdot 10^1 = 10^2...$
  • $\vdots$
  • $10^k \text{ units}\; = 10^k\cdot 10^0 = 10^{k-1}\cdot 10^1 = \cdots = 10^1 \cdot 10^{k-1} = 10^0\cdot 10^k = 10^k$

Likewise one tenth of a unit = $10^{-1}$...etc.

In this sense, there is a sort of "hierarchy of powers of 10" with powers in correspondence with the integers, but I don't know how expressing it as such might be helpful or useful.

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