The Importance Of Significant Figures In Statistics

The significant figures in a number are the digits that contribute to the precision of its value. Since measurements are approximations, significant figures are critical when reporting data because it demonstrates to what precision the data was measured. As a result, certain rules must be set into place to determine which digits in a value are significant and how to calculate values that express the correct number of significant figures.

For numerical values, there are rules set to in order to determine which digits are significant. All non-zero numbers are considered significant. Zeroes to the right of a decimal point and zeroes located within nonzero numbers in a numerical value, such as 3008 or 30.01 are also significant. However,

All digits that one is confident about should be recorded plus one more digit that had been estimated based upon the device. The last digit recorded is an approximation. For example, if an object is measured with a ruler with millimeter markings to be between 4.5 and 4.6 cm., an extra digit must be assessed. Recording a number with fewer or greater significant digits would not be an accurate representation of the data gathered.

The number of significant figures is directly related to the measurement. Since accuracy refers to how close the measured value is to the actual number, the values are only as accurate as the device used. Significant figures tell us more about the precision of a measurement. Results are limited by the precision of the data. If results are passed back and forth, the correction precision information is also passed

If a calculation involves only addition and/or subtraction, then the Addition/Subtraction rule must be used. This rule states that the calculated value must be rounded off to the same decimal place as the least precise item of data. For example, if the calculation was 4.150 + 1.2, then the answer, 5.35, would be rounded off to the tenths place to be 5.4. If the calculation involves multiplication and/or division, then the Multiplication/Division rule must be used which states that the calculated value must be rounded off to contain the same number of significant figures as the least precise item of data. 4.25 x 1.3 would be rounded off to 5.5. In a multistep calculation involving both addition and/or subtraction and multiplication and/or division, then the Multiplication/Division rule must be followed. However, every time addition or subtraction is being performed, the addition/subtraction rule must be used to figure out how many significant figures are in the answer. That value is then used in subsequent calculations.

An “exact” number is a number that is exact by definition. Examples include a count of a number of objects, such as 5 pens or a dozen eggs, or as conversion factors e.g. 1 calorie is equal to 4.184 joules. Exact numbers do not have any uncertainty so they do not influence the number of significant figures in a calculated