Orders of Magnitude
Key Questions

The mathematical explanation is to take the base ten log of a number and floor it, however, that's just a fancy math way of saying count the digits before the decimal marker then take 1.

Answer:
It depends on what you mean by "order of magnitude".
Explanation:
In one meaning, it is a number's nearest power of 10.
For example,
#9.9 × 10^2# is much closer to#10^3# than to#10^2# , so we say that the order of magnitude is#3# .By the same argument,
#9.9 × 10^3# is closer to#10^2# than to#10^3# , so we say that the order is#3# .In another meaning, it is a difference of
#1# unit in the exponent of#10# in the value of a quantity.Thus,
#2315# is one order of magnitude larger than#231.5# , and#23.15# is one order of magnitude less than#231.5# .If the value of a number decreased from
#2315# to#23.15# , we would say that it decreased by two orders of magnitude or that the values differed by two orders of magnitude.In that sense, a difference in orders of magnitude is always expressed as a positive number.