The sentence "'I know that.' is correct and usable in written English.
It can be used when one is responding to a statement or a question that they understand or agree with. For example, if someone said "Tigers are one of the most powerful animals in the world," you could respond with "'I know that.'".
Exact(60)
I know that feeling.
"I know that look.
"I know that place.
Even I know that".
How do I know that?
"I know that pretty well.
"I know that sounds cheesy.
"I know that sounds weird.
I know that "veil" is.
"I know that sounds pretentious.
I know that very well.
More suggestions(5)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com