Hindu-Arabic numerals (or simply "Arabic numerals") are the standard numbers used in most of the world. They are named this way because they were first introduced by the Hindu people of India, then came by way of the Arabs (who added the important concept of zero; however, some sources have it that the Indians added this themselves) to the western world, where it supplanted earlier number systems such as Roman numerals.
Confusingly, the "Arabic" numbers used by the western world are different in appearance from the forms used in Arabic-speaking countries, though the basic system is the same. It is a particular point of confusion that the Arabic-script digit "5" looks like a zero to Westerners. Similarly, there are different forms of the numerals in use in India.
The major innovation of the Arabic system over earlier number systems is the use of place value for the digits. A number is written as a series of digits from most-significant at the left to least-significant at the right, where each digit represents a value one-tenth of what that same digit would represent one place to the left, or ten times what that digit would represent one place to the right; in other words, the digits are multiplied by powers of ten. This is known as "base ten" (presumably chosen in ancient times due to humans normally having ten fingers to count on).
If the number has a fractional part, it can be represented with a decimal point after the units digit and succeeding digits representing tenths, hundredths, and so on. The character used for the decimal point varies by country; Americans use a dot (.), while some other countries use a comma (,). Since many programming languages were developed by Americans, the dot is typically used there. For formatting purposes, it is common to put a separator between groups of three digits in numbers with four or more digits, and in countries that use a dot for a decimal point, a comma is often used here, and vice versa. Spaces or apostrophes are sometimes used as a separator to display numbers in a country-neutral way.
It is possible to use the same digits to represent numbers in other bases (consisting of multiples of the powers of different numbers from 10), as frequently done by mathematicians and programmers. Bases less than 10 can be expressed with a subset of the normal digits, like 0-7 for octal and 0-1 for binary. For bases higher than 10, additional digits need to be introduced. Hexadecimal, used often by programmers, has a standard representation that uses the letters A through F to represent digits with values 10 through 15. Base64, used as a transfer encoding for binary data, puts 64 different printable ASCII characters into service as digits.
There are a few standard notations used in computer science to indicate which base a number is expressd in. Often, an extra leading zero before a number indicates octal, and "0x" before a number indicates hexadecimal. Other notations include a suffix "h" after a hexadecimal number, or a dollar sign ($) before a hexadecimal number.