In writing, I am confused about when to use "into" (one word) vs. "in to" (two words). Could you please explain to me when to use one vs. the other? Will you also use each one in a sentence?

Thank you
I went into the shop
I went in to see the doctor

I think 'into' is used when the subject 'physically' goes inside the object, where as 'in to' is used when you have an infinitive, i.e. 'to see', 'to do' and so forth.

Please correct me if I'm wrong and expand on what I've left out...
In, Into In indicates location or condition; into indicates movement or a change in condition. They found the lost letters in a box after moving into the house.
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Chuck - Thank you for your comments. That sounds exactly right. It's been a while since my days in English class. My fabulous teachers would be horrified to know I had forgotten any grammar rules. Your use of 'in to' and 'into' in sentences cleared up my confusion immediately.