structural:summarization, information:extraction
India

Pingala (c. 3rd or 2nd century BC), a Sanskrit prosody scholar, 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 meter, a notation similar to Morse code. Pingala used the Sanskrit word śūnya explicitly to refer to zero.

The concept of zero as a written digit in the decimal place value notation was developed in India. A symbol for zero, a large dot likely to be the precursor of the still-current hollow symbol, is used throughout the Bakhshali manuscript, a practical manual on arithmetic for merchants. In 2017, researchers at the Bodleian Library reported radiocarbon dating results for three samples from the manuscript, indicating that they came from three different centuries: from AD 224–383, AD 680–779, and AD 885–993. It is not known how the birch bark fragments from different centuries forming the manuscript came to be packaged together. If the writing on the oldest birch bark fragments is as old as those fragments, it represents South Asia's oldest recorded use of a zero symbol. However, it is possible that the writing dates instead to the time period of the youngest fragments, AD 885–993. The latter dating has been argued to be more consistent with the sophisticated use of zero within the document, as portions of it appear to show zero being employed as a number in its own right, rather than only as a positional placeholder.

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 this text, śūnya ("void, empty") is also used to refer to zero.

The Aryabhatiya (c. 499), states sthānāt sthānaṁ daśaguṇaṁ syāt "from place to place each is ten times the preceding".

Rules governing the use of zero appeared in Brahmagupta 's Brahmasputha Siddhanta (7th century), which states the sum of zero with itself as zero, and incorrectly describes division by zero in the following way:

A positive or negative number when divided by zero is a fraction with the zero as denominator. Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero.