Is it Present Continuous "- Be careful - I AM BEING careful"?
It was taken from the film where a boy is helping his father on the board of the board to put up a mast. His father says "Be careful" The son responds "I am being careful". It is simply present continuous, yes?

Question

Is it Present Continuous "- Be careful - I AM BEING careful"?
It was taken from the film where a boy is helping his father on the board of  the board to put up a mast. His father says "Be careful" The son responds "I am being careful". It is simply present continuous, yes?

Answer

The boy says: "I AM being careful", with emphasis on AM.

Yes, it is correct. 
I am being careful = I am acting or doing things in a very careful manner.

Answer

If there is something that you are doing now or something that is happening now that for which you are being careful, then you would say:
"I am being careful"
If you are generally careful all the time, you would just say:
"I am careful."
If you wanted to emphasize it you would say:
"I am always careful."

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