# Decimal Floating Point

Decimal floating point arithmetic refers to both a representation and operations on decimal floating point numbers. Working directly with decimal (base 10) fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions (common in human-entered data, such as measurements or financial information) and binary (base 2) fractions.

The advantage of decimal floating-point representation over decimal fixed-point and integer representation is that it supports a much wider range of values. For example, while a fixed-point representation that allocates eight decimal digits and two decimal places can represent the numbers 123456.78, 8765.43, 123.00, and so on, a floating-point representation with eight decimal digits could also represent 1.2345678, 1234567.8, 0.000012345678, 12345678000000000, and so on. This wider range can dramatically slow the accumulation of rounding errors during successive calculations; for example, the Kahan summation algorithm can be used in floating point to add many numbers with no asymptotic accumulation of rounding error.

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