Preferred number

In industrial design, preferred numbers (also called preferred values, preferred series or convenient numbers) are standard guidelines for choosing exact product dimensions within a given set of constraints. Product developers must choose numerous lengths, distances, diameters, volumes, and other characteristic quantities. While all of these choices are constrained by considerations of functionality, usability, compatibility, safety or cost, there usually remains considerable leeway in the exact choice for many dimensions.

Preferred numbers serve two purposes:

Preferred numbers represent preferences of simple numbers (such as 1, 2, and 5) and their powers of a convenient basis, usually 10.

In 1870 Charles Renard proposed a set of preferred numbers. His system was adopted in 1952 as international standard ISO 3. Renard's system divides the interval from 1 to 10 into 5, 10, 20, or 40 steps. The factor between two consecutive numbers in a Renard series is approximately constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (approximately 1.58, 1.26, 1.12, and 1.06, respectively), which leads to a geometric sequence. This way, the maximum relative error is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10.

In applications for which the R5 series provides a too fine graduation, the 1-2-5 series is sometimes used as a cruder alternative. It is effectively an R3 series rounded to one significant digit:

This series covers a decade (1:10 ratio) in three steps. Adjacent values differ by factors 2 or 2.5. Unlike the Renard series, the 1-2-5 series has not been formally adopted as an international standard. However, the Renard series R10 can be used to extend the 1-2-5 series to a finer graduation.

This series is used to define the scales for graphs and for instruments that display in a two-dimensional form with a graticule, such as oscilloscopes.

The denominations of most modern currencies, notably the euro and British pound, follow a 1-2-5 series. The United States and Canada follow the series 5, 10, 25, 50, 100 (cents), and also $5 and $10 which belong to the same series. However, after that comes $20, not $25. The ¼-½-1 series (... 0.1 0.25 0.5 1 2.5 5 10 ...) is also used by currencies derived from the former Dutch gulden (Aruban florin, Netherlands Antillean gulden, Surinamese dollar), some Middle Eastern currencies (Iraqi and Jordanian dinars, Lebanese pound, Syrian pound), and the Seychellois rupee. However, newer notes introduced in Lebanon and Syria due to inflation follow the standard 1-2-5 series instead.

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