Hindu–Arabic numeral system
The base-ten positional numeral system that uses ten symbols, including zero, with each digit’s value determined by its place.
Place-value notation: A numeral system in which a symbol’s value depends on its position. Each digit’s position assigns its power of ten in this system.
Brahmi numerals: An ancient Indian numeral system whose symbols contributed to the later forms of the digits. Their evolving forms are ancestors of several Hindu–Arabic numeral symbols.
Arithmetic: The branch of mathematics concerned with numbers and operations such as addition, subtraction, multiplication, and division. The system’s place values make written arithmetic procedures efficient.
Abacus: A counting device that represents numbers with movable counters or beads. It supported calculation before written positional numerals became widespread and remained useful alongside them.
Unary numeral system: A numeral system that represents a number by repeating a single mark once for each unit. Unlike this compact positional system, unary notation has no place values or zero placeholder.
Decimal numeral system: A numeral system based on ten, with successive place values differing by powers of ten. This system is the familiar positional form of base ten.
Indian numerals: Numeral forms developed in India that became the basis of the Hindu–Arabic system. The system’s decimal place-value structure and zero emerged from Indian mathematics.
Long multiplication: A written algorithm for multiplying multi-digit numbers by combining partial products. Its shifted partial products directly reflect the value of each digit’s place.
Roman numerals: A numeral system using letters such as I, V, X, L, C, D, and M, without place value. Their additive notation makes written calculation less compact than Hindu–Arabic numerals.
Sexagesimal: A positional numeral system based on sixty, used historically in astronomy and still in time and angle measurement. It shares place value but organizes digits by powers of sixty rather than ten.