"For all intents and purposes" is the correct phrase according to American usage. The British version of the idiom is "To all intents and purposes." (See the Related link.)
A practical purpose is a purpose that is achievable, efficient and contributes to the greater good or generally beneficial to an individual or group.
An analytical purpose is the intention to...
Science can be applied for practical purposes by its nature of answering questions about the natural world, using logical inferences, evidence and hypotheses to obtain a theory and explanation....