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Decimal Expansion

Basic definition

The decimal expansion of a number is the usual "base 10" representation of a real number.

Detailed definition

The decimal expansion of a number is its representation in base-10 (i.e., in the decimal system). In this system, each "decimal place" consists of a digit 0-9 arranged such that each digit is multiplied by a power of 10, decreasing from left to right, and with a decimal place indicating the 10^0 = 1s place. For example, the number with decimal expansion 1234.56 is defined as 1234.56 | = | 1×10^3 + 2×10^2 + 3×10^1 + 4×10^0 + 5×10^(-1) + 6×10^(-2) | = | 1×1000 + 2×100 + 3×10 + 4 + 5×1/10 + 6×1/100. Expressions written in this form sum_k b_k 10^k (where negative k are allowed as exemplified above but usually not considered in elementary education contexts) are said to be in expanded notation.

Related terms

base | binary | decimal | decimal period | decimal point | expanded notation | fraction | Midy's theorem | multiplicative order | regular number | repeating decimal | unique prime

Related Wolfram Language symbol

RealDigits

Educational grade level

elementary school level (California grade 2 standard)

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