When I see a number like "183" the first thing I see is a "1". If I'm looking very quickly, perhaps scanning a column of numbers, that might be all I see, and I'll approximate this number as "100" when "200" would be closer. Yes, truncation isn't the same thing as rounding, but wouldn't things be a lot easier if it were? Let's make it be that way.

To interpret a number today, you multiply each column by the size it represents and add them up:

number	100s	10s	1s	sum
100	1	0	0	1*100 + 0*10 + 0*1
120	1	2	0	1*100 + 2*10 + 0*1
121	1	2	1	1*100 + 2*10 + 1*1
129	1	2	9	1*100 + 2*10 + 9*1
125	1	2	5	1*100 + 2*10 + 5*1

With this new system, we still do this, but in each column our available options range from -5 to 4 instead of 0 to 9.

number	100s	10s	1s	sum
100	1	0	0	1*100 + 0*10 + 0*1
120	1	2	0	1*100 + 2*10 + 0*1
121	1	2	1	1*100 + 2*10 + 1*1
129	1	3	-1	1*100 + 3*10 + -1*1
125	1	3	-5	1*100 + 3*10 + -5*1

Here are a few more examples:

old notation	new notation
0	0
4	4
7	1-3
579	1-4-2-1
432	432
1999	200-1

And here's a program to calculate these:

def to_new_notation(x):
  digits = []
  carry = False
  for digit in reversed([
        int(x) for x in str(x)]):
    if carry:
      digit += 1
      carry = False

    if digit >= 5:
      digit -= 10
      carry = True

    digits.append(digit)

  if carry:
    digits.append(1)

  digits.reverse()
  return digits

Update 2016-05-25: Truncation isn't actually rounding in this system unless you allow both 5 and ^-5 as digits. Thanks to Marius for pointing this out.

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