Round numbers anywhere in a JSON document

I want to compare lots of JSON-Documents without caring about a precision more then 2 digits. I want to round any number in a JSON-Document, but I do not know where in the documents numbers are (but they are not keys).
I'm currently just using a regex (sed 's/\(\.[0-9][0-9]\)[0-9]*/\1/g'), but like this, 0.9999 or 1.0001 do have the same result.

I know how to do it when I know in which paths numbers are, but how do I do it, if I do not specify any location of numbers in the document?

From this source:

{"a": -4e-12,"b": {"c": 0.999999999999997,"d": 101.12222222222  }}

I'd expect a result like:

{"a": 0,"b": {"c": 1,"d": 101.12  }}