In India the decimal place-value notation matured into a complete arithmetic in which a small set of digits, their meaning set by position, could express any number. The crucial step was treating zero as a number in its own right rather than a mere gap: a written zero appears in the Bakhshali manuscript and on the Gwalior temple inscription of 876 CE, and in 628 CE the astronomer Brahmagupta gave the first formal rules for calculating with zero and negative numbers. This combination of positional notation and an operational zero made long multiplication, division and algebra tractable. The system later passed through the Islamic world to Europe as the 'Hindu–Arabic' numerals.
It is the foundation of all later calculation used to survey land, levy taxes, divide estates and compute the dimensions of buildings, fortifications and city layouts. Without an operational zero and place value, the quantitative basis of planning and engineering would be unworkable.
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