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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 Wolfram Language symbol

    RealDigits

    Educational grade level

    elementary school level (California grade 2 standard)

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