Rules for rounding in decimal numbering

I participated in a Business to Business (B2B) project, where I was part of the team that developed the backoffice platform, and another team developed Frontoffice (the e-commerce store). Each part of the platform - Back and Front Office needed to exchange data and it was necessary to establish a numbering rounding rule, defining decimal places, for the calculations of orders with freight percentages, platform comission and taxes.

Every software that performs numerical calculations in the financial context needs to determine rounding of decimal places.This is necessary by market convention, or by law.

Therefore it is necessary to define rules to be followed so that the results can be foreseen and audited.

Another example of the need to establish rules for numbering rounding, in the context of computer systems occurs when there is communication between systems, with data exchange.

To meet all these contexts, the Brazilian Association of Technical Standards - ABNT, for rounding decimal numbering, can be applied effectively.

Read here what is the difference between back office and front office

When to numeric round the decimal places

In statistics related calculations, financial mathematics among other situations where software solves everyday problems, business or even in the context of education and that are related to the use of numbers with decimal place limits.

Rules for rounding in decimal numbering

To define standard in the numerical rounding of decimal places, the Brazilian Association of Technical Standards (ABNT), establishes the NBR 5891:2014 to this. However, there is a standard universal rule used by many programming languages.

Simple rule for rounding decimal places

When the digit to be conserved is followed by a digit less than 5, the digit remains conserved and the posterior ones removed. When it is larger than 5, it adds a 1 to the digit you want to round.

Example: To round 3 decimal places in 2 in the number 7,421, as the third digit is 1, less than 5, keep the second digit, the number 2, and remove the third one, resulting in 7.42.
Example: To round 3 decimal places in 2 in the number 7.425, as the third digit is 5, superior or equal to 5, add 1 to the second digit, result 7.43.

ABNT NBR 5891/2014

The normative establishes the following points for this rule:

When the digit to be conserved is followed by a digit less than 5, the digit remains conserved and the posterior ones removed.
- Example: To round 3 decimal places in 2 in the number 7,421, as the third digit is 1, less than 5, the second digit, the number 2 is kept and the third, is eliminated, resulting in 7.42.
When the digit to be conserved is followed by a digit greater than 5, or equal to 5 followed by at least one digit different from zero, a unit is added to the digit to be conserved and the posterior ones are removed.
- Example: Round to two decimal places the number 23,52621. The third number is tested, the number 6, as is greater than or equal to 5, adds 1 to the second digit which is the number 2, resulting in 23.53.
- Example: Round to two decimal places the number 5,8451, as the third digit is 5, followed by a different number of zero 0, the second house is rounding more 1, resultingIn: 5.85.
When the digit to be kept is odd, followed by 5 and later of zeros, adds a unit to the digit to be conserved and the posterior ones are removed.
- Example: Round to four decimal places the number 4,3241500, the result is: 4,3242.
When the digit is conserved to be pair, followed by 5 subsequently of zeros, the digit remains to be conserved and the later removed.
- Example: Round to one decimal digit the number 4,850, the result is: 4.8.