**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.

Read more about Decimal Floating Point: Implementations, IEEE 754-2008 Encoding, Floating Point Arithmetic Operations

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“Mildred Pierce: You look down on me because I work for a living, don’t you? You always have. All right, I work. I cook food and sell it and make a profit on it, which, I might *point* out, you’re not too proud to share with me.

Monte Beragon: Yes, I take money from you, Mildred. But not enough to make me like kitchens or cooks. They smell of grease.

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—Ranald MacDougall (1915–1973)

“It makes little sense to spend a month teaching *decimal* fractions to fourth-grade pupils when they can be taught in a week, and better understood and retained, by sixth-grade students. Child-centeredness does not mean lack of rigor or standards; it does mean finding the best match between curricula and children’s developing interests and abilities.”

—David Elkind (20th century)

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—Henry David Thoreau (1817–1862)