Extra digits after the point signal precision, not vanity
Decimal notation uses base ten, now standard worldwide through Hindu–Arabic positional digits. Writing 1.320 milligrams implies tighter measurement bounds than 1.32. Decimals approximate every real number: add digits and you shrink the error, though fractions like one-third never terminate.
A decimal system uses ten as its radix. The Hindu–Arabic positional system is today's global standard for integers and fractions, though Roman and Chinese numerals remain non-positional alternatives. A decimal numeral may be an integer like 2017 or include a separator—dot or comma—for fractional parts such as 20.70828.
Decimal fractions are rational numbers a/10ⁿ. Examples include 0.8 (= 8/10), 3.14159 (= 314159/100000), and 1/3, which cannot terminate because three is not a power of ten. Terminating decimals end in zeros; repeating decimals like 5.123144144... represent rationals with eventually periodic digits.
In science, digit count hints at measurement precision. Mass given as 1.32 mg suggests truth between 1.315 and 1.325 mg, while 1.320 mg narrows the window to 1.3195–1.3205 mg. The trailing zero in 4.690 versus 4.69 is meaningful when computing √22 to three decimal places.
Ancient civilizations used ten and its powers—Egyptian, Brahmi, Greek, Hebrew, Roman, and Chinese systems—likely because humans count on ten fingers. Hindu–Arabic notation solved large-number multiplication and division, then extended to decimal fractions. Every real number admits decimal approximations with error at most 10⁻ⁿ for any chosen n. Reduced to lowest terms, a fraction ends cleanly in decimal only when its denominator is built from twos and fives alone, so 1, 2, 4, 5, 8, 10, 16, 20 and 25 all qualify. Some endless expansions even name the same value twice: a tail of nines collapses into the next digit up, the familiar puzzle of 0.999... equalling one. In computing, a leading zero is sometimes dropped, as in .1234, a habit ordinary writing avoids because the lone dot is easy to miss.
Source: Decimal
