Analytical test results should be reported in the format prescribed in the study plan. If no format is specified test results should be reported to the same number of decimal places as the specification, for example if a specification is 95.0 to 105.0 % then a result of 99.617% should be reported as 99.6%.

When calculating results all available figures should be used and the final result rounded according to established procedures.

Usual Rounding Procedure

The usual rounding procedure is to truncate the number to one more decimal place than the specification, thus 99.617 % is truncated to 99.61%, and the final 7 is discarded.

The value is then rounded to the required number of decimal places according to the following rounding rules.

If the figure in the final decimal place is 1 to 4 the last figure is discarded, for example 99.61 % is rounded to 99.6 %.

If the figure in the final decimal place is 6 to 9 the figure preceding the last figure in increased by one, thus 99.68 % is rounded to 99.7 %.

Rounding of Numbers – Tie brake Rules

If the final figure in the truncated result is 5 as in 99.65 %, there is a statistically equal chance that the number preceding the 5 could be either 6 or 7. In such a case it is necessary to establish a tie brake rule.

There are a number of such rules including:

• Rounding up, where the number preceding the last number is always rounded up, to give 99.7 % in the above example
• Rounding down, where the final number is discarded, to give 99.6 % in the above example
• Rounding to even, if the number preceding the last number is even, then the last figure is discarded, thus 99.65 % would be rounded to 99.6 %. However, if the number preceding the final number is odd it is increased by one thus, 99.75 % would be rounded to 99.8 %

Which tie brake rule is selected, will depend on the needs of the analysis, client or the laboratory.

The United States Pharmacopeia mandates that the first rule (rounding up) is applied.

However, the third rule (rounding to even) is used by most computer programs and is the default rounding mode in the Institute of Electrical and Electronic Engineers (IEEE) Standard 754, “Computing Functions and Operators”.