Why are fractions used in the imperial system instead of decimals?

Answer 1

Most of the units in the imperial system are based on numbers other than 10 (eg 1 foot = 12 inches). When converting a fraction (in simplest terms) to a decimal it will ONLY be a terminating decimal if the denominator has prime factors ONLY of 2 and/or 5.

eg 12 has prime factors: 12 = 22 x 3.

The 3 is enough to ensure that the decimal representation of twelfths (ie the decimal representation of inches as part of a foot) will normally be repeating decimals (unless the numerator also has a prime factor of 3, ie 3/12, 6/12, 9/12 which simplify to remove the factor 3 from the denominator) and these can only be written as an approximation.

Imperial units were devised when [electronic] calculators were a thing of the future and calculations were all done by hand, and were usually based on some physical measure. It may be surprising, but working with fractions can actually be much easier than working with decimals (especially when NOT using a calculator), along with giving more accurate results.

In the course I am currently doing, an example came up at my last tutorial: when calculating something, a fraction of 2/3 came up which was then divided into 1,500,000. By using an approximate decimal for the 2/3 of 0.6666 (or 0.6667) the result was inaccurate (~2,250,225 or ~2,249,888) compared to using the fraction itself; the result could be obtained from another route which gave the exact amount - the same as when using the fraction: 1,500,000 ÷ 2/3 = 1,500,000 x 3/2 = 2,250,000.