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I was curious whether a clear-cut definition of order of magnitude for a number exists.

I have seen several posts in this forum touching upon, or tapping from, the concept of order of magnitude. None seemed (to me) to address the definition, though; for example Order of Magnitude, What does "within the same order of magnitude" convey?, Order of magnitude of a variable..

The ideal answer should assist the naive user in discriminating whether 50.1, or 99, should be of order 10 rather than order 100, for example. Or, at least, show why a clear-cut answer does not exist.

XavierStuvw
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    An "order of magnitude" is usually used in the case of a very large number. In this case, a number "close" to the given number is determined. I do not think that there is a definition covering all cases because the approximation is usually chosen depending on how large the given number is. – Peter Aug 01 '17 at 18:30
  • google gives :

    or·der of mag·ni·tude noun noun: order of magnitude; plural noun: orders of magnitude a class in a system of classification determined by size, each class being a number of times (usually ten) greater or smaller than the one before. "values might be compared by order of magnitude, a staple in making ballpark estimates" relative size, quantity, quality, etc. "the new problems were of a different order of magnitude" the arrangement of a number of items determined by their relative size. "the items are arranged in ascending order of magnitude"

     –  Aug 01 '17 at 20:00
  • A bit of cross-pollination with discussions in the Physics forum: https://physics.stackexchange.com/questions/16322/confront-order-of-magnitudes, https://physics.stackexchange.com/questions/107088/order-of-magnitude, – XavierStuvw Aug 07 '17 at 08:19

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