The Core Rule for Multiplication and Division
When multiplying or dividing numbers, the result should have the same number of significant figures as the measurement with the fewest significant figures. This is often referred to as the 'least precise' rule because your answer cannot be more precise than your least precise input measurement.
Understanding the Principle
This rule is crucial for reflecting the uncertainty inherent in measurements. Since a chain is only as strong as its weakest link, a calculation's precision is limited by the measurement that was taken with the least accuracy. Including more digits than justified would imply a level of precision that doesn't exist.
Practical Example of the Rule
Consider calculating the area of a rectangle with a measured length of 12.3 cm (3 significant figures) and a width of 4.5 cm (2 significant figures). Multiplying 12.3 cm by 4.5 cm yields 55.35 cm². According to the rule, since 4.5 cm has only two significant figures, the final area must be rounded to two significant figures, resulting in 55 cm².
Importance in Scientific Reporting
Adhering to significant figure rules ensures that all reported data accurately represent the reliability of the measurements taken. It prevents misrepresentation of experimental precision and allows scientists to correctly evaluate the validity and comparability of different experimental results, maintaining integrity in scientific communication.