Some examples of the implementation of the above principles during rounding are listed in the table below: Here are the three rules:Rule 1: If the last digit to be deleted is less than 5, the last digit remains unchanged. If rounding is required, consider a single digit to the decimal place to the right of the last digit of the limit printout. If this figure is less than 5, it is eliminated and the previous figure remains unchanged. If this figure is equal to or greater than 5, it shall be eliminated and the previous figure shall be increased by 1 (1). Table I: Excel 2010 results with four examples. Many labs use Microsoft Excel for calculations, so it`s interesting to see how it compares to the four examples. Excel has three rounding functions: rounding, rounding, and rounding. For each function, the number to be rounded and the number of decimal places required must be specified. Excel 2010 results for the 2 decimal example are shown in Table I. Incorrectly rounded values are highlighted in yellow.

The rounding function works well, except for example 4. However, Excel can be easily programmed to automatically perform an unbiased rounding decision tree. For example, suppose the values to round begin in cell C9 and the number of decimal places to round in cell E9. These values of X, Y, and Z are stored in the corresponding rows (9 to 12) of columns G, H, and I. The rounding formula (a nested “if” formula) is now placed in cell J9 for the first example and copied down for lines 10, 11 and 12 for the others: Each time rounded downwards, the USP General Leaflets, the European Pharmacopoeia (Ph. Eur), the British Pharmacopoeia (BP) should be mentioned to ensure that rounding is not misleading, to replace an erroneous result with a successful one. 1.1 Establish a procedure for establishing guidelines for the reporting of analytical values and rounding. Note: The general rules for rounding and reporting numerical values are as follows (exceptions to these rules are those indicated otherwise in the monograph, SOP or TSP). Table II: Results of the unbiased rounding formula with Excel.The Excel results of the unbiased rounding formula are presented in Table II and are consistent with manual evaluation for the four examples. The best explanation for unbiased rounding is found in a textbook published by Columbia University`s Statistical Research Group in 1947 (2). The editor, Churchill Eisenhart of the National Bureau of Standards (at the time), was one of the most influential statisticians of his time. 2.1 Analytical Chemist – Quality Control – Responsible for indicating analytical values and rounding figures in accordance with these guidelines.

Chris BurgessRounding a result to the required number of decimal places is easy, isn`t it? After all, we`ve all been taught in college or university that only two rules are necessary. Figure 1: Decision tree for an unbiased rounding process. It is usually easier to see how such a rule works when you draw it in a decision tree, as shown in Figure 1. In this figure, we determine the number or number to be rounded by X, the digit or number to be deleted by Y, and the difference between the truncated value and the complete numerical value by Z. Based on the values of X, Y and Z, we can make the right rounding decision without bias. By rounding to three decimal places, values become zero We can now test our unbiased rounding process using four examples. Of course, rounding only takes place after the final calculation. The general opinions of the USP clearly specify this requirement: the last example may be surprising because it would be considered erroneous under the simple rules. However, it is unlikely to find such an example in the analysis unless the method can only yield 5 or 0 for Y. The problem is that simplicity is not always correct. From a statistical point of view, the application of Rule 2 will discourage the data over time, as there is always rounding, especially if 5 is often the number to be rounded.

4 and below and 6 and more are balanced in rounding, but what about 5? It has been known for more than 60 years that applying only Rules 1 and 2 leads to data distortion. More interestingly, the third rule was known at least to statisticians of the time. Unfortunately, this rule is rarely, if ever, mentioned in modern manuals and guidelines. · If the result is < 50 ppm, indicate it with 1 decimal place in the 1st round π with 7 significant numbers to 2 decimal places. 3.2. The calculated analytical values shall be indicated in the worksheets, certificates of authenticity and raw data sheets as indicated in the table below:. 1. USP 35, General Notes 7.20, "Rounding Rules" (US Pharmacopeial Convention, Rockville, MD, 2012). For example: in 354 = 3, 5 and 4 are significant numbers 2.

C. Eisenhart, M.W. Hastay, W.A. Wallis, Selected Techniques of Statistical Analysis, (McGraw-Hill, New York, 1947). Rule 2: If the last digit to be deleted is greater than 5 or 5 followed by digits greater than 0, the last digit retained is incremented by 1. 3.1 Once the analysis is complete, the analytical chemist calculates the analytical result in the worksheet and compares it to the limits specified in the specification. Rounding and reporting methodology for some important analytical parameters Please do not spam. Comments with links will not be published. 2) In 0.0961 = 0 (to the right of the decimal point), 9, 6 and 1 are significant numbers Editable pharmaceutical documents in MS Word format for drugs: Dosage values for API, active and inactive excipients should be reported in mg and percentage. 3.2. If the calculated value(s) contain more digits to one decimal place than to the specified limit, the figures shall be rounded to one decimal place as described below.

Excel`s truncation function can be used to extract values from X, Y, and Z. with the formulas: Pingback: SOP for reviewing analytical report and raw data – Pharma Beginners IF(AND($H 9>=5.$I 9>=0),ROUNDUP($C 9.$E 9); ROUNDING($C 9.$E 9)))) Expressed in mg (or other similar units) to the decimal place that supports the % value in the specification. Interns: Quality Control Chemists / Section Heads ✔ Global Regulatory Updates ✔ Pharmaceutical News Interview ✔ Questions and Answers ✔ All guidelines in one place · Symbols such as > (more than), < (less than) cannot be used. Instead, the same is reported in words like,. For Y = TRUNC($C 9.$E 9+1)*10^($E 9+1)-TRUNC($C 9.$E 9)*10^($E 9+1) Note: However, these clauses do not apply to middleweights. Conversion of the number of units to weight (kg/g, etc.): 3.2.2 If the known impurity is less than the LOD, disregard it in the calculation.