Most phone numbers are seven digits long, and this fits within the memory span of digits for most people. when is it to convert the numbers into the letters on the phone keypad? how does such a conversion relate to memory span?

It is helpful to convert phone numbers into letters when you are advertising for a business.  For example, if you were advertising for a fish market, the phone number could be something like "123-FISH".  This is helpful to remember the numbers for a lot of people.  It's a lot more likely someone will remember  "123-FISH" than a bunch of random numbers.

Hope this helps!!