Arabic numerals

Arabic numerals, in common usage, means representation of the digits of the decimal system by the signs 0 1 2 3 4 5 6 7 8 9.

However, it would be inaccurate to think of this number system just in terms of decimal, rather, it is a completely well-defined system of numbers that pertains to any base, and not just base ten (decimal).

The mathematician who defined this system and is generally considered the father of this numbering system is Al-Khwarizmi, who was not actually an Arab himself, but a muslim. He is also the father of algebra. He was an Iranian mathematician who published most of his works in the Arabic language, the de facto scientific language of that time.

For instance, when we write 125, today, by default, we assume 125 in base 10, or decimal, and this is how it is constructed:

5x10^0 + 2x10^1 + 1x10^2 == 5 + 20 + 100 == 125 (in decimal)

but if we were talking about 125 in base 8, then it would be:

5x8^0 + 2x8^1 + 1^8^2 = 5 + 16 + 64 = 85 (in decimal)

so 125 in base 10 (decimal) = 125 (decimal) but 125 in base 8 (octal) = 85 (decimal)

For a given base N, there are N symbols of representation. So in base 10 there are 10 symbols, that in most countries 0, 1, 2 ... 9 are used, but the symbols themselves are just symbols, and any symbols could be used, without changing the fundamental concept. So for instance, instead of using "0,1, 2, 3, 4, 5, 6, 7, 8, 9" for the 10 symbols of base 10, we could use "a, b, c, d, e, f, g, h, i, j" instead .... and in that case, then "125" in base 10, would be written as "bcf", but the numeric value of that number, and also how it is worked out in this number system, would reamin unchanged.

The binary system (base 2) that we use in computers today is simply the base 2 of this system. So in base two, there are only two symbols of representation, which normally "0" and "1" are used:

11001 in binay = 1x2^0 + 0x2^1 + 0x2^2 + 1x2^3 + 1x2^4 = 1+0+0+8+16 = 25 (decimal)

This number system is the most fundamental and perhaps the greatest inventions of all time which forever changed the way humans think about numbers, and is the foundation of our scietific and mathematical world as we know it today.

European, Arabic and Indic numerals

Using Arabic-Indic digits, numbers are written with the most significant digit on the left, just like it is with European digits.

External links:

Unicode reference glyphs for Arabic (See code U+0660-U+0669, U+06F0-U+06F9)
Unicode reference glyphs for Devanagari (See code U+0966-U+096F)
Unicode reference glyphs for Tamil (See code U+0BE6-U+0BEF)