https://www.sulprobil.de/tags/how-likely-does-rounding-values-alter-their-rounded-sum/ Recent content in How Likely Does Rounding Values Alter Their Rounded Sum on Sulprobil Hugo en Sat, 13 Jun 2026 08:52:00 +0100 https://www.sulprobil.de/rounding_values_alters_their_sum_en/ Sat, 13 Jun 2026 08:52:00 +0100 https://www.sulprobil.de/rounding_values_alters_their_sum_en/ <h2 id="abstract">Abstract</h2> <p>How likely is it that a sum of rounded values is not identical to their rounded sum?</p> <p>For two random floating point numbers this is obvious: The likelihood is around 25% - that is the percentage of red in this picture:</p> <p><img src="https://www.sulprobil.de/likelihood_of_an_altered_sum_by_rounding_two_values.png" alt="Two Values"></p> <p>But it might be somewhat surprising that the likelihood approaches 90% if you round and add more and more numbers:</p> <p><img src="https://www.sulprobil.de/percentage_of_altered_sum.png" alt="Rounding Values alters their Sum"></p> <p>With seven floating point numbers the likelihood is already larger than 50% that the sum of rounded values is not equal to their rounded sum.</p>