Decimal place value in India

During the first millennium CE, Indian mathematical and astronomical traditions developed sophisticated decimal computation. A digit takes its value from its position, with units, tens and hundreds differing by factors of ten. A small set of signs can therefore represent very large numbers. Sanskrit works also used number words and other systems suited to verse. Written calculation, recitation and worked procedures operated together, requiring readers to translate numerical relationships in a text into arithmetic operations.

References: [1]

Place-value notation must retain a position even when it contains no quantity. A sign for an empty place distinguishes, for example, units from hundreds separated by an absent tens value. Zero also became a number with its own rules of operation. Digit shapes varied across scripts, materials and regions. Their ordered positions allowed addition, carrying and borrowing to follow the same procedures for integers of very different sizes.

References: [1]

Astronomers used large numbers and fractions for cycles, angles and dates, while arithmetic works treated distribution, exchange and geometry. Decimal methods entered Arabic scholarship through translation and explanation of algorithms. Latin works later introduced related procedures, and copying and printing changed the forms of the digits. Hindu-Arabic numerals gradually spread through European commerce and education. The positional structure became a shared basis for modern written arithmetic and many calculating tools.

References: [1]