Number Notation Converter (US, European, Swiss, Indian, Scientific)

It is a historical convention rather than a logical one. The decimal point spread out of late-1500s Europe alongside Simon Stevin's decimal arithmetic, and printers used whatever mark was easiest to set in their type: a dot in Britain, a comma in much of continental Europe, an apostrophe in Switzerland. When ISO 31-0 tried to harmonise the world on the comma it failed, because by then every country's tax forms, contracts, and accounting software were already locked in. So we ended up with a patchwork that the SI standard formalises as 'either dot or comma is allowed, just be consistent'.

A lakh is one hundred thousand (100,000) and a crore is ten million (10,000,000). The grouping reflects this: the rightmost three digits form the thousands group, then every group to the left is two digits because each step up the scale is a factor of one hundred, not one thousand. The convention is much older than the Western thousand/million system; it appears in Vedic Sanskrit texts as part of the dasagunottara (powers of ten) sequence, and survived into modern Indian English because the underlying place-value vocabulary was already so entrenched in trade and accounting.

Both put a number in the form coefficient times ten-to-the-power, but they differ in which exponents are allowed. Scientific notation forces the coefficient to be between 1 and 10, so the exponent is whatever it needs to be (5.972 times 10 to the 24 for Earth's mass). Engineering notation restricts the exponent to multiples of three, which lines up cleanly with the SI prefixes kilo, mega, giga, micro, nano, and so on. Engineers prefer it because '47 times 10 to the 3 ohms' immediately reads as '47 kilo-ohms'. Pure scientists prefer scientific because the coefficient always sits between 1 and 10, which makes significant-figure bookkeeping simpler.

It dates from the punch-card and teletype era of the 1950s, when programming languages like FORTRAN needed to write scientific notation on input devices that did not have a superscript or a multiplication sign. The letter e (for 'exponent') was chosen because it was already on every keyboard and would not be confused with a digit or arithmetic operator. The convention spread to every programming language and to most spreadsheet software, which is why a CSV file from any system on Earth will happily round-trip a value like 6.022e23 even though no human ever writes the letter e in a hand-written calculation.

Two reasons. First, the names of large numbers above a billion diverge between the short scale (used in the US and most of the English-speaking world: billion = 10^9) and the long scale (still used in much of continental Europe: billion = 10^12). Second, languages without a built-in name for every power of ten have to chain together compound words, and at some point everyone gives up: there is no widely agreed name for 10 to the 36, for instance, even though the SI prefix system runs out at quetta (10^30) on purpose. For audit-level certainty, contracts usually include both the spelled-out and the numeric forms and treat the numeric form as authoritative if they disagree.