Decimals extend place-value notation to parts of a whole. The number 3.14 means 3 ones, 1 tenth, and 4 hundredths. Each position to the right of the decimal point represents a negative power of ten. The system is a natural extension of the way we write whole numbers.

Decimal fractions became common in Europe only after Simon Stevin's work in the sixteenth century. Before that, traders used fractions or sexagesimal notation. The decimal point itself varies by region: some countries use a comma instead.

Decimals can be terminating, like 0.25, or repeating, like 0.333... Repeating decimals correspond to rational numbers. Irrational numbers have non-repeating, non-terminating decimal expansions. In computation, decimals are often approximated with a fixed number of digits, which introduces rounding error. Understanding that limit is part of working with numerical methods.

• Base-ten representation with a decimal point
• Positions represent powers of ten
• Can terminate or repeat
• Irrational numbers have non-repeating expansions