Sunday, July 15, 2018

[cftaqxzh] Digit groupings of increasing size

Although grouping digits in groups of 3 is useful for quickly telling how large a medium-sized number is (perhaps up to a trillion = 1e12), after a number gets too large, it becomes difficult to count how many groups of three it has.  Therefore, consider grouping in larger chunks as the number gets larger.  Below we demonstrate grouping digits in groups of 3, 4, 8, 16, 32,... doubling in powers of 2.  The partial sums are powers of 2 minus 1, so it is easy to go from the number of groups to the total digits in them.

Could also do Fibonacci sequence, triangular numbers, square numbers.

Not sure how useful this is: for transcribing a number, digit groupings of constant size is best.  If you want to convey the order of magnitude of a number, scientific notation is best (or tetration).

Previously similar.

9,123 ~= 9e3

9,1234,123 ~= 9e7

9,12345678,1234,123 ~= 9e15

9,1234567890123456,12345678,1234,123 ~= 9e31

9,12345678901234567890123456789012,1234567890123456,12345678,1234,123 ~= 9e63

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