Make Truncation be Rounding

May 22nd, 2016
ideas, math
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.

Comment via: google plus, facebook, substack

Recent posts on blogs I like:

Elixir's Last Dance

On May 18th, the contra dance band Elixir had their last gig ever. The dance was packed: there were three hundred people. It was the only dance BIDA has ever done where they sold tickets. People flew from across the country just to hear Elixir play one la…

via Lily Wise's Blog Posts June 5, 2025

Body Language For Trans People

When I first came out as trans, resources for trans people were full of advice about body language.

via Thing of Things June 2, 2025

Workshop House case study

Lauren Hoffman interviewed me about Workshop House and wrote this post about a community I’m working on building in DC.

via Home April 30, 2025

more     (via openring)