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Roman numerals are the numbers represented by letters

ex. I, V, X, L, C, D, M etc.

Hindu Arabic numerals are the numbers that are numerical

ex. 1,2,3,4,5,6,7,8,9 etc.

Roman numbers work on a dual base system, alternately 5 and 2.

I=1, V=5 and X=10. 1,2,3,4,5,6,7,8,9,10 are I,II,III,IV,V,VI,VII,VIII,IX,X.

Notice that 4 is not IIII, but IV and 9 is not VIIII but IX. The rule is that whenever a number is preceded by a smaller one, the smaller one is to be subtracted.

Notice also that every 2 or 5 step has its own letter - the system can not express numbers bigger than those for which it was designed.

The Hindu-Arabic system has a single base : ten. Also it is a positional number system. The array of letters in complex combinations used by the Romans is gone. The Romans used I,X,C,M for 1,10,100,1000. The Hindu-Arabic system used 1 for all of these. The difference came from the position of the 1. In the rightmost place it was 1. 2nd from the right it was 10. 3rd from the right it was 100, and so on. At first the Arab system used a dot ( . ) to indicate an empty place; 3 was 3, 3 . was 30, 7 . 4 was 704 and so on, etc., und so weiter.

It worked much better than the Roman system, except that the small dots could easily be lost, or even found where they were not originally written. The dot was replaced by 0, and meant the same as the dot - "nothing here".

The zero probably came from a Hindu mathematician; it is unclear whether it was the invention of zero that caused the replacement of the dot, or whether the realization that the 0 signified nothing sparked the invention of the very concept of zero.

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