paikkalasku

Paikkalasku is the place-value numeral principle used in mathematics to represent numbers. In a positional system, the value of a digit depends on its place within the number. In the decimal system, digits 0 through 9 occupy positions that correspond to powers of ten: ones, tens, hundreds, thousands, and so on. The position acts as a multiplier; a digit d in the k-th position from the right stands for d × 10^k. Zero is used as a placeholder, which makes it possible to distinguish, for example, 507 from 57 and enables simple arithmetic.

Example: 5072 = 5×1000 + 0×100 + 7×10 + 2×1.

The same principle applies in other bases: in base-2, digits 0 or 1 occupy positions that are powers of two; in base-16, digits 0–9 and A–F occupy positions that are powers of sixteen. Paikkalasku is foundational in arithmetic and number understanding; it underpins algorithms for addition, subtraction, multiplication, and division, and it explains why digits must be aligned by place during computations.

Historically, the modern place-value approach stems from the Hindu-Arabic numeral system, which introduced zero as a placeholder and a base-10 structure. It spread through the Islamic world to Europe by the Middle Ages, replacing earlier non-positional numeral systems such as Roman numerals. In Finnish education, paikkalasku is taught as a core concept from early grades to help students grasp magnitude and perform arithmetic reliably.