0

As a numerical digit, 0 plays a crucial role in decimal notation: it indicates that the power of ten corresponding to the place containing a 0 does not contribute to the total.

The modern use of 0 in this manner derives from Indian mathematics that was transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci.

[3] The Italian mathematician Fibonacci (c. 1170 – c. 1250), who grew up in North Africa and is credited with introducing the decimal system to Europe, used the term zephyrum.

The Italian word zefiro was already in existence (meaning "west wind" from Latin and Greek Zephyrus) and may have influenced the spelling when transcribing Arabic ṣifr.

In a tablet unearthed at Kish (dating to as early as 700 BC), the scribe Bêl-bân-aplu used three hooks as a placeholder in the same Babylonian system.

[11][12] The Babylonian positional numeral system differed from the later Hindu–Arabic system in that it did not explicitly specify the magnitude of the leading sexagesimal digit, so that for example the lone digit 1 () might represent any of 1, 60, 3600 = 602, etc., similar to the significand of a floating-point number but without an explicit exponent, and so only distinguished implicitly from context.

[13] The Mesoamerican Long Count calendar developed in south-central Mexico and Central America required the use of zero as a placeholder within its vigesimal (base-20) positional numeral system.

[citation needed] Quipu, a knotted cord device, used in the Inca Empire and its predecessor societies in the Andean region to record accounting and other digital data, is encoded in a base ten positional system.

However, after using the Babylonian placeholder zero for astronomical calculations they would typically convert the numbers back into Greek numerals.

[24] By AD 150, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero (—°)[25][26] in his work on mathematical astronomy called the Syntaxis Mathematica, also known as the Almagest.

[30] The earliest use of zero in the calculation of the Julian Easter occurred before AD 311, at the first entry in a table of epacts as preserved in an Ethiopic document for the years 311 to 369, using a Ge'ez word for "none" (English translation is "0" elsewhere) alongside Ge'ez numerals (based on Greek numerals), which was translated from an equivalent table published by the Church of Alexandria in Medieval Greek.

[31] This use was repeated in 525 in an equivalent table, that was translated via the Latin nulla ("none") by Dionysius Exiguus, alongside Roman numerals.

As noted in the Xiahou Yang Suanjing (425–468 AD), to multiply or divide a number by 10, 100, 1000, or 10000, all one needs to do, with rods on the counting board, is to move them forwards, or back, by 1, 2, 3, or 4 places.

[41] Chinese authors had been familiar with the idea of negative numbers by the Han dynasty (2nd century AD), as seen in The Nine Chapters on the Mathematical Art.

[42] Pingala (c. 3rd or 2nd century BC),[43] a Sanskrit prosody scholar,[44] used binary sequences, in the form of short and long syllables (the latter equal in length to two short syllables), to identify the possible valid Sanskrit meters, a notation similar to Morse code.

[46][49][50] The Lokavibhāga, a Jain text on cosmology surviving in a medieval Sanskrit translation of the Prakrit original, which is internally dated to AD 458 (Saka era 380), uses a decimal place-value system, including a zero.

In AD 813, astronomical tables were prepared by a Persian mathematician, Muḥammad ibn Mūsā al-Khwārizmī, using Hindu numerals;[61] and about 825, he published a book synthesizing Greek and Hindu knowledge and also contained his own contribution to mathematics including an explanation of the use of zero.

[61] Muhammad ibn Ahmad al-Khwarizmi, in 976, stated that if no number appears in the place of tens in a calculation, a little circle should be used "to keep the rows".

[63] The Hindu–Arabic numeral system (base 10) reached Western Europe in the 11th century, via Al-Andalus, through Spanish Muslims, the Moors, together with knowledge of classical astronomy and instruments like the astrolabe.

The Italian mathematician Fibonacci or Leonardo of Pisa was instrumental in bringing the system into European mathematics in 1202, stating: After my father's appointment by his homeland as state official in the customs house of Bugia for the Pisan merchants who thronged to it, he took charge; and in view of its future usefulness and convenience, had me in my boyhood come to him and there wanted me to devote myself to and be instructed in the study of calculation for some days.

One popular manual was written by Johannes de Sacrobosco in the early 1200s and was one of the earliest scientific books to be printed, in 1488.

The digit 0 with a dot in the center seems to have originated as an option on IBM 3270 displays and has continued with some modern computer typefaces such as Andalé Mono, and in some airline reservation systems.

A further distinction is made in falsification-hindering typeface as used on German car number plates by slitting open the digit 0 on the upper right side.

The number 0 is also used in several other ways within various branches of mathematics: The value zero plays a special role for many physical quantities.

This is in contrast to temperatures on the Celsius scale, for example, where zero is arbitrarily defined to be at the freezing point of water.

[83][84] Measuring sound intensity in decibels or phons, the zero level is arbitrarily set at a reference value—for example, at a value for the threshold of hearing.

Modern computers store information in binary, that is, using an "alphabet" that contains only two symbols, usually chosen to be "0" and "1".

Binary coding is convenient for digital electronics, where "0" and "1" can stand for the absence or presence of electrical current in a wire.

[85] Computer programmers typically use high-level programming languages that are more easily intelligible to humans than the binary instructions that are directly executed by the central processing unit.

[98] In comparative zoology and cognitive science, recognition that some animals display awareness of the concept of zero leads to the conclusion that the capability for numerical abstraction arose early in the evolution of species.