"order of magnitude" is a deliberate way to present something as a rough estimate.
In that way it is a non-mathematical form of big-O notation.
You might prefer saying 10x or whatever, but complaining about the base is unnecessarily pedantic.
Edit: Actually, Wikipedia even says In its most common usage, the amount being scaled is 10 and the scale is the (base 10) exponent being applied to this amount (therefore, to be an order of magnitude greater is to be 10 times as large).
In that way it is a non-mathematical form of big-O notation.
You might prefer saying 10x or whatever, but complaining about the base is unnecessarily pedantic.
Edit: Actually, Wikipedia even says In its most common usage, the amount being scaled is 10 and the scale is the (base 10) exponent being applied to this amount (therefore, to be an order of magnitude greater is to be 10 times as large).