It's difficult to explain the difference between knowledge and understanding. There's overlap between the two. They aren't as different as apples and trains. You can know they're different but understanding the nature of this difference can be illusive.
Knowing/knowledge comes from learning facts. Understanding is deeper. It's a mental process of comprehending the meaning of the facts. This may not be a good example but: You can know the world started from a big bang because you've read/learned it, but understanding this is different.
I'll try another. You can know Jack and Jill love each other but you may not understand it.
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memorizing is seeing bits and pices of the picture. knowing is seeing the whole picture. knowing is the understanding of what you have memorized.
(Full) Comprehension, (absolute) understanding, knowing
It can be, rarely, as in a knowing look. (one that implies understanding)Knowing is the present participle of the verb to know, and may be a verb, an adjective, or a noun (gerund).
The dimensional analysis has several other advantages which include 1)increase of understanding, 2) knowing what is important, and 3)compacting the presentation
I study math through mastering the basic skills and knowing the different formulas and also by understanding the given problem... that's all