Decimal expansion

A representation of a number as a sequence of decimal digits multiplied by powers of ten. It may terminate or continue infinitely, with repeating or nonrepeating digits.

Place value: A positional numeral system assigns each digit a value determined by its position. Each decimal digit contributes a multiple of a power of ten according to its position.
Euclidean division: The expression of an integer as a quotient times a divisor plus a remainder. At each step of decimal long division, the remainder determines the next digit.
Decimal representation of rational numbers: The correspondence between rational numbers and terminating or eventually repeating decimal expansions. A reduced fraction terminates in base ten exactly when its denominator has no prime factors besides 2 and 5.
Binary numeral system: A positional numeral system that uses the digits 0 and 1 and powers of two. Binary expansions use powers of two where decimal expansions use powers of ten.
Base-10 numeral system: A positional numeral system that uses ten as its base and the digits 0 through 9. Decimal expansions use powers of ten because their underlying positional system has base ten.
Repeating decimal: A decimal expansion in which a finite block of digits repeats indefinitely. A repeated remainder in division forces the subsequent decimal digits to cycle.
Decimal representation of irrational numbers: The representation of irrational real numbers by infinite, nonrepeating decimal expansions. These expansions encode values exactly even though no finite decimal gives the full number.
Scientific notation: A notation expressing a number as a coefficient multiplied by an integer power of ten. Scientific notation rearranges decimal place value to represent very large or small numbers compactly.
Rational number: A number expressible as the quotient of two integers with a nonzero denominator. Rational numbers have decimal expansions that terminate or eventually repeat.
Terminating decimal: A decimal expansion with only finitely many nonzero digits after the decimal point. Division terminates when a remainder becomes zero, leaving a finite decimal representation.

Linked from 10 pages