# Rules for Rounding off Analytical results

The 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: **

- 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:**

- 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
- 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:**

- A weight reading of 27.375 g rounded off to 2 decimal places will read 27.38 as seven is an odd number
- 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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