Why Does Double Precision Show 17 Decimal Places for Some Repeating Decimals?

Double Precision: Exploring Decimal Representation Accuracy

Double precision, a data type commonly used in programming, offers a claimed precision of approximately 15 decimal places. However, when dealing with values represented as repeating decimals, such as 1.0/7.0, anomalies arise.

Why 17 Decimal Places?

Internally, double precision numbers possess 53 significant bits, which translates to approximately 15.95 decimal digits. While this should theoretically lead to 16 decimal places of representation, implementations round down to 15 (denoted by DBL_DIG).

To illustrate, the nextafter() function can reveal the nearest representable numbers adjacent to a given value. When applied to 1.0/7.0 (0.14285714285714285), we observe 17 displayed decimal places. The change in the last digit indicates the actual precision of the representation.

Precision and Chance

In the case of 1.0/7.0, the last displayed digit coincidentally matches the mathematical value (5). However, for other repeating decimals (e.g., 1.0/3.0), the last digit may not align, showcasing the limitations of precise decimal representation.

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