Hindu-Arabic numerals, which are now used internationally, were adopted by most European countries about 500 years ago. This system was discovered in India. It is not known who discovered them, or exactly when they were discovered. The system evolved into a system similar to that which we use now between around 200 B.C. and 500 A.D. There are several ancient Indian manuscripts that use these numerals, such as the Bakhshali manuscript (third or fourth century) and the Lokavibhaga (458 A.D.). By the sixth or seventh century they were in common use in India.
The earliest mention of these numbers in the West was in 662 A.D. in a work by Severus Sebokht, where he writes:
I will omit all discussion of the science of the Hindus, a people not the same as the Syrians, their subtle discoveries in the science of astronomy, discoveries that are more ingenious than those of the Greeks and the Babylonians; their computing that surpasses description. I wish only to say that this computation is done by means of nine signs. If those who believe because they speak Greek, that they have reaced the limits of science should know these things, they would be convinced that there are also others who know something.
Hindu-Arabic numerals were adopted by the Arabs starting around 750 A.D., and around 820 the Arab mathematician Al-Khowarizmi used them in his calculations (see the Arab math history page for a tiny bit more information on Al-Khowarizmi). This system, which started to gain acceptance in Europe around 1200, was only fully accepted in Europe in the 16th century.
The advantage of Hindu-Arabic numerals over Roman numerals can be instantly appreciated. Any number of any magnitude can be expressed accurately and fairly briefly using only ten symbols. Furthermore, Hindu-Arabic numerals have a straightforward positional principle of addition or multiplication.
Note that the term "Arabic numerals" is also sometimes used to refer to the
style used to write numbers that is still current throughout the Arabic
and Persian-speaking worlds. The shape of many of these numerals, while
similar to that used in the Western world, is somewhat different. For
example, here are the numbers 1 through 10 written in Arabic numerals:
Alternately, you might have been looking for names for the numbers 1–10 in Arabic.
Sources used (see bibliography page for titles corresponding to numbers): 37.