# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Calculator Time and Angle Work**

**From:**Paul Hirose

**Date:**2017 Sep 5, 13:27 -0700

In the era of mechanical calculating machines, the "rule of 40" was a trick to force a base 10 machine to add or subtract in base 60. For instance, to calculate 1°40′ + 2°30′, add 140 and 230. The result, 370, is clearly wrong since minutes are not in the legal range. You fix that by adding 40, which rolls the minutes over, forces a carry into degrees, and shows the correct sum: 410 (4°10′). Inspection of the sum alone doesn't always indicate when the result needs adjustment, however. For instance, if you add 50.5′ + 55.5′ the calculator says the result is 1060 (1°06.0′). The minutes are in the legal range but the result is wrong! You must add 400 to obtain the correct sum: 1460 (1°46.0′). This situation occurs whenever the sum of the minutes is 100 or greater, and thus is easy to detect by a glance at the operands. That last example shows the rule of 40 is valid with degrees and decimal minutes, if you take care to align the 40 with the proper columns. The rule of 40 is applicable to subtraction too. You subtract 40 to force a borrow into that column. It may help avoid confusion if you use the decimal point to separate degrees and minutes. That's what I do, so the rule of 40 becomes the rule of .4.