The unique thing I think I have is that I visualize long strings of digits as notes on a musical scale. 735 is high-low-middle. I have found I can retain strings of up to 15 or so digits in short-term memory by chunking them into triplets and memorizing them as arpeggio chords, or by their relative positions.
I see numbers as notes. So each unique number - say my college ID, my aunt's cell number or my driving license is a MIDI tune in my head.
Also, visually each number is like a 'identity' - not a numeral. When I had a image processing class, running an edge detector on binary images was fun. I could guess the potrait/image just looking at the numbers (just like how you'd guess animal shapes in a connect-the-dots game)
I have all my important numbers memorized - SIN, multiple credit cards, driver's license, library card, health cards, all my financial account numbers, and the same for my partner. Do you do that too?
Only digits have notes associated with them. A number like 1000 is just four notes in a row. Irrational numbers again are just composed of their digits.