I understand how integer and floating point data types are stored, and I am guessing that the variable length of decimal data types means it is stored more like a string.
Does that imply a performance overhead when using a decimal data type and searching against them?
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Pavel has it quite right, I'd just like to explain a little.
Presuming that you mean a performance impact as compared to floating point, or fixed-point-offset integer (i.e. storing thousandsths of a cent as an integer): Yes, there is very much a performance impact. PostgreSQL, and by the sounds of things MySQL, store DECIMAL / NUMERIC in binary-coded decimal. This format is more compact than storing the digits as text, but it's still not very efficient to work with.
If you're not doing many calculations in the database, the impact is limited to the greater storage space requried for BCD as compared to integer or floating point, and thus the wider rows and slower scans, bigger indexes, etc. Comparision operations in b-tree index searches are also slower, but not enough to matter unless you're already CPU-bound for some other reason.
If you're doing lots of calculations with the DECIMAL / NUMERIC values in the database, then performance can really suffer. This is particularly noticeable, at least in PostgreSQL, because Pg can't use more than one CPU for any given query. If you're doing a huge bunch of division & multiplication, more complex maths, aggregation, etc on numerics you can start to find yourself CPU-bound in situations where you would never be when using a float or integer data type. This is particularly noticeable in OLAP-like (analytics) workloads, and in reporting or data transformation during loading or extraction (ETL).
Despite the fact that there is a performance impact (which varies based on workload from negligible to quite big) you should generally use numeric / decimal when it is the most appropriate type for your task - i.e. when very high range values must be stored and/or rounding error isn't acceptable.
Occasionally it's worth the hassle of using a bigint and fixed-point offset, but that is clumsy and inflexible. Using floating point instead is very rarely the right answer due to all the challenges of working reliably with floating point values for things like currency.
(BTW, I'm quite excited that some new Intel CPUs, and IBM's Power 7 range of CPUs, include hardware support for IEEE 754 decimal floating point. If this ever becomes available in lower end CPUs it'll be a huge win for databases.)
