^† You can think of counting in standard Roman numerals as an increment function (“add ‘I’ to the end”) and some rewrite rules to apply sequentially to the end of the Roman numeral:

• IIII → IV / ____#
• IVI → V / ____#
• VIV → IX / ____#
• IXI → X / ____#

Similarly:

• XXXX → XL / ____#
• XLX → L / ____#
• LXL → XC / ____#
• XCX → C / ____#

And of course:

• CCCC → CD / ____#
• CDC → D / ____#
• DCD → CM / ____#
• CMC → M / ____#

So, starting at CLXXXVIII (188) and incrementing by I to CC (200) we get:

• CLXXXVIII + I = CLXXXVIIII
  • IIII → IV / ____#, giving CLXXXVIV
  • VIV → IX / ____#, giving CLXXXIX
    
    
• CLXXXIX + I = CLXXXIXI
  • IXI → X / ____#, giving CLXXXX
  • XXXX → XL / ____#, giving CLXL
  • LXL → XC / ____#, giving CXC
    
    
• CXC + I = CXCI
  
  
• CXCI + I = CXCII
  
  
• CXCII + I = CXCIII
  
  
• CXCIII + I = CXCIIII
  • IIII → IV / ____#, giving CXCIV
    
    
• CXCIV + I = CXCIVI
  • IVI → V / ____#, giving CXCV
    
    
• CXCV + I = CXCVI
  
  
• CXCVI + I = CXCVII
  
  
• CXCVII + I = CXCVIII
  
  
• CXCVIII + I = CXCVIIII
  • IIII → IV / ____#, giving CXCVIV
  • VIV → IX / ____#, giving CXCIX
    
    
• CXCIX + I = CXCIXI
  • IXI → X / ____#, giving CXCX
  • XCX → C / ____#, giving CC

Honestly, it seems pretty straightforward when you look at it like this, but people still don’t seem to like it. This also goes to show that most subjects are amenable to linguisticky interpretation if you look hard enough. Ah, Linguistics! Is there anything it can’t do!?

^‡ Alas, D is already taken, but G’s similarity in shape to C makes for a pleasantly felicitous alternative.

^‡† Note that a number of nattering nobodies insinuate that this makes nine somehow “naughty by nature”. Nincompoops!

^‡‡ In Canada, Z would be an acceptable alternative for the value of 1, but only when dealing with quantities of 41.

^‡‡† Of course there is a superior, novel solution, but it’s usually best to let your nerd try to figure it out for themselves.

For those among the curious for whom the superior, novel solution isn’t immediately obvious...

The legacy system has 1-based I–X–C–M and 5-based V–L–D, to which we’ve added 2-based J–Y–G–N. Adding more simple symbols (as opposed to the typographically challenging apostrophus or vinculum) just makes sense. For the 1-based and 2-based extensions, we add similarly shaped pairs: E/F (10,000 and 20,000), H/K (100,000 and 200,000), O/Q (1,000,000 and 2,000,000), P/R (10,000,000 and 20,000,000), and S/Z (100,000,000 and 200,000,000). We can extend the 5-based run by taking graphemic inspiration from the apostrophus and adding W (a doubled V = 5,000), T (a flipped and doubled L = 50,000), B (stacked Ds = 500,000), A (flipped, barred V = 5,000,000), U (rounded V = 50,000,000), and finally ß (similar to S and Z, which are maximally valued in their respective runs = 500,000,000).

For those who need to go farther, I propose a more typographically propitious billion (10⁹) multiplier—the grave accent—giving the series Ì–X̀–C̀–M̀–È–H̀–Ò–P̀–S̀ (1 billion to 100 quadrillion), J̀–Ỳ–G̀–Ǹ–F̀–K̀–Q̀–R̀–Z̀ (2 billion to 200 quadrillion), and V̀–L̀–D̀–Ẁ–T̀–B̀–À–Ù–ß̀ (5 billion to 500 quadrillion). While that it sufficient for many of one’s more pedestrian numerical needs, it is by no means the end of the show!

The quintillion (10¹⁸) multiplier, the acute accent, gives Í to ß́. The octillion (10²⁷) multiplier, a dot above, gives İ to ß̇. The undecillion (10³⁶) multiplier, a diaeresis, gives Ï to ß̈. The quattuordecillion (10⁴⁵) multiplier, a tilde, gives Ĩ to ß̃. The septendecillion (10⁵⁴) multiplier, a breve, gives Ĭ to ß̆. The vigintillion (10⁶³) multiplier, an inverted breve, gives Ȋ to ß̑.

Once you get to numbers of a reasonable size, the silly names like million, billion, vigintillion, jillion, and godzillion become more a hindrance than a help, so we continue on with just good ole scientific notation.

• a circumflex indicates a multiplier of 10⁷² (Î to ß̂)
• a caron indicates a multiplier of 10⁸¹ (Ǐ to ß̌)
• a macron indicates a multiplier of 10⁹⁰ (Ī to ß̄)
• a ring indicates a multiplier of 10⁹⁹ (I̊ to ß̊)
• a prime indicates a multiplier of 10¹⁰⁸ (I̍ to ß̍)
• a double prime indicates a multiplier of 10¹¹⁷ (I̎ to ß̎)
• a left half ring indicates a multiplier of 10¹²⁶ (I͑ to ß͑)
• a right half ring indicates a multiplier of 10¹³⁵ (I͗ to ß͗)
• a left arrow indicates a multiplier of 10¹⁴⁴ (I᷾ to ß᷾)
• a right arrow indicates a multiplier of 10¹⁵³ (I͐ to ß͐)
• a comma indicates a multiplier of 10¹⁶² (I̓ to ß̓)
• an x indicates a multiplier of 10¹⁷¹ (I̽ to ß̽)
• a bridge indicates a multiplier of 10¹⁸⁰ (I͆ to ß͆)

Moving any of the multipliers below the symbol gives a further multiplier of 10¹⁸⁰:

• I̖ I̗ Ị I̤ Ḭ I̮ I̯ I̭ I̬ I̱ I̥ I̩ I͈ I̜ I̹ I͔ I͕ I̦ I͓ I̪ (10¹⁸⁹–10³⁶⁰)

For those who actually use moderately large numbers, two further series of multipliers are available:

• Ȉ I̋ I᷀ I᷁ I͌ I̐ I͒ I҅ I҆ I᷄ I᷅ I᷆ I᷇ I᷈ I᷉ Ỉ I̒ I̔ I̿ Ḯ (10³⁶⁹–10⁵⁴⁰)
• I̫ I̼ I᷂ I͙ I̻ I̝ I̞ I̙ I̘ I̟ I͚ I̢ I̡ Į I̧ I͍ I͎ I͉ I̳ I̺̺ (10⁵⁴⁹–10⁷²⁰)

Finally we reach the limit of the current system, with a few more modifiers, including a hint at ways to extend it further, bringing in stylistic variants, like bold, italic, double-struck, fraktur, and encircled:

• I͛ I᷃ I̾ I͋ I͊ I I 𝕀 𝕴 Ⓘ (10⁷²⁹–10⁸¹⁰)

Some will complain that these distinctions are typographically too subtle, and perhaps they are—though polytonic Greek was a great success, no? At the very least they provide an opportunity for your science nerd to become familiar with processing Unicode programmatically. Another win-win!

Below is a table with all of the diacritics proposed in this superior, novel solution—enlarged and applied to I for simplicity and clarity.

^‡‡‡ Tractable. That’s a word the engineering types seem to like. Put those sociolinguistics skills to good use and sprinkle in those shibboleths so you bond with your victim target new friend!