a long list of values upwards. For an integer in rounding, replace the digits after the n digit with zeros. For example, if 1254 is rounded to 2 significant figures, then 5 and 4 are replaced to 0 so that it will be 1300. For a number with the decimal point in rounding, remove the digits after the n digit. For example, if 14.895 is rounded to 3 significant figures, then the digits after 8 are removed so that it will be 14.9. In financial calculations, a number is often rounded to a given number of places. For example, to two places after the decimal separator for many world currencies. This is done because greater precision is immaterial, and usually it is not possible to settle a debt of less than the smallest currency unit. In UK personal tax returns, income is rounded down to the nearest pound, whilst tax paid is calculated to the nearest penny. As an illustration, the decimal quantity 12.345 can be expressed with various numbers of significant figures or decimal places. If insufficient precision is available then the number is rounded in some manner to fit the available precision. The following table shows the results for various total precision at two rounding ways (N/A stands for Not Applicable). Another example for 0.012345. (Remember that the leading zeros are not significant.) The representation of a non-zero number x to a precision of p significant digits has a numerical value that is given by the formula: where which may need to be written with a specific marking as detailed above to specify the number of significant trailing zeros. Writing uncertainty and implied uncertainty Significant figures in writing uncertainty It is recommended for a measurement result to include the measurement uncertainty such as , where xbest and σx are the best estimate and uncertainty in the measurement respectively. xbest can be the average of measured values and σx can be the standard deviation or a multiple of the measurement deviation. The rules to write are: σx has only one or two significant figures as more precise uncertainty has no meaning. 1.79 ± 0.06 (correct), 1.79 ± 0.96 (correct), 1.79 ± 1.96 (incorrect). The digit positions of the last significant figures in xbest and σx are the same, otherwise the consistency is lost. For example, in 1.79 ± 0.067 (incorrect), it does not make sense to have more accurate