Rules for Rounding off Analytical results

Rules for Rounding off Analytical results

Analytical-ResultsThe results of analysis are expressed by two quantities. First is the numerical quantity and the other is a unit of measurement. The results of most analysis are calculated manually or displayed by the system in digital format. More often the results are displayed in integers and decimals. Beyond a certain number of decimal points the numbers lose their significance so it becomes necessary to round off the results so as to make the results more meaningful and understandable.

Principles of rounding off results

Rule – 1 – When the digit succeeding the number to be retained is less than 5, the retained digit remains unchanged.

Example:

  1. The result of assay is 99.992% is to be rounded off to 2 decimal places. As 2 in the third decimal places is less than 5 rounding to 2 decimal places on rounding off it becomes 99.99%

Rule – 2 – When the digit succeeding the number to be retained is more than 5, the retained digit is increased by 1

Examples:

  1. The result of loss of drying is 1.437 and is to be rounded off to 2 decimal places. As 7 is more than 5 the result is expressed as 1.44
  2. The result of essay is 99.998% and needs to be rounded off to 2 decimal places. As 8 in the third decimal place is more than 5 the assay on rounding off to 2 decimal places will become 100 .00%

Rule – 3 – When the digit succeeding the digit to be retained is 5or 5 followed by 0’s the figure to be retained shall be (a) increased by 1if it is odd and (b) unchanged if even. For this purpose 0 is regarded as an even number.

Example:

  1. A weight reading of 27.375 g rounded off to 2 decimal places will read 27.38 as seven is an odd number
  2. A weight reading of 27.345 rounded off to 2 decimal places will read 27.34 as 4 is an even number.

General rounding off conventions

  • Results of assay, LOD, weight, specific gravity, ash content, moisture are usually expressed in 2 decimal places.
  • Results of impurity are rounded off to 3 decimal places

The results of all analysis should fall within acceptable limits determined by comparison with analysis of standards traceable to established sources. Uncertainty of measurements will be discussed in a subsequent article.

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