Why 36 bits?
Many early computers aimed at the scientific market had a 36-bit word length. This word length was just long enough to represent positive and negative numbers to an accuracy of ten decimal digits (actually 35 bits would have been the minimum). It also allowed the storage of six alphanumeric characters. Prior to the introduction of computers, the state of the art in precision scientific and engineering calculation was the ten-digit, electrically-powered, mechanical calculator, such as those manufactured by Frieden, Marchant and the Monroe Calculator Company. These calculators had a column of keys for each digit and operators were trained to use all their fingers when entering numbers, so while some specialized calculators had more columns, ten was a practical limit. Computers, as the new kid on the block, had to match that accuracy.
Early computers with 36-bit words included the MIT Lincoln Laboratory TX-2, the IBM 701/704/709/7090/7040 series and the Digital Equipment Corporation PDP-6, PDP-10 and DECSystem-20 machines. Smaller machines, like the PDP-9 and PDP-15 used 18-bit words so a double word would be 36-bits. Decimal computers sold in that era, such as the IBM 650 and the IBM 7070, had a word length of ten digits.
By the time IBM introduced System/360, scientific calculations had shifted to floating point and mechanical calculators were no longer a competitor, so the 360's practice of using word lengths that were a power of two quickly became universal.