are 3.4 and .1 in the same order of magnitude
That depends on how exactly you defined an order of magnitude.
Does this article help you?
So, does the entire number make up the order of magnitude or just the decimal places.
Just the decimal places? I think 8.5 and 8.47395 are of the same order of magnitude, but the decimal places are respectively 1 and 5...
From my understanding after reading the wikipedia article 0.1 is of magnitude -1 while 3.4 has an order of magnitude of 0. To work out the order of magnitude you can write the number in standard form, the power of ten when it is in standard form is the magnitude.
An order of magnitude difference is different though. 3.4 is 34 times as big as 0.1, so it is two orders of magnitude bigger (round log34 to the nearest integer).
This is just my understanding from quickly reading the wikipedia article, so what I've said should be taken with a pich of salt (as should anything from wikipedia).
Edit: Gokul43201 pointed out an error I made. I think it is now correct (though you still shouldn't assume that everything I've said is completely accurate).
Order of Magnitude tells you the Scale of a number. Decimal places is about Precision.
x and y have the same Order of Magnitude, but y has more Precision.
When talking orders of magnitude or anything involving comparisons in terms of factors (ratios being more important than differences), you do not round off arithmetically - you round off numbers geometrically.
Also, what's important with OoMs is the word "about" you find in the mathworld definition - there's fudge factor involved. But if you want to go with a purist definition of an OoM, (which is a silly waste of time, in my opinion) two numbers are within an OoM of each other if the larger ratio of the numbers(b/a, if b>a) is smaller than 10.
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