I'm not sure if it should be "ni juu san sen man" or "ni sen san byaku man".
For the zero method, do you count all decimal places following the leading number, or only the decimal places that are actually zero? (i.e. in the above example, would we say 23,000,000 has six zeros, or seven zeros?)
There is a shortcut for remembering the large numbers. Just remember the three numbers below as they are. It is introduced in Course 1 Pre-lesson B "Counting".
10まん (JUU MAN) - hundred thousand unit 100まん (HYAKU MAN) - one million unit 1000まん (ISSEN MAN) - ten million unit
Twenty million is 2000まん (NI-SEN MAN) and three million is 300まん (SAN-BYAKU MAN). So you say 2300まん (NI-SEN SAN-BYAKU MAN).
There is another way of counting large numbers (It is just my way though.) Just take the last 4 zeros away (23,000,000⇒2300) and say the remaining number (2300/NI-SEN SAN-BYAKU) and the unit まん (MAN) together. Does it work for you?
Please remember that a different unit is used for "one-hundred million", which is いちおく (ICHI OKU).
Mr. Trombley has a very good video on exactly this (numbers 4) I think ni juu san sen man does not exist. That would be ni oku san sen man. So yes, ni sen san hyaku man, I believe. Here is the link to the video. https://www.youtube.com/watch?time_continue=1&v=is3aJAlhHWo