* Precision refers to how close repeated measurements are to each other. A more precise measurement has less variation.
* Significant figures are the digits in a measurement that contribute to its precision. They are all the digits that are known with certainty, plus one uncertain digit.
How Significant Figures Determine Rounding:
1. Counting Significant Figures:
* Non-zero digits: Always significant.
* Zeros:
* Zeros between non-zero digits are significant (e.g., 10.03 has 4 significant figures).
* Zeros at the end of a number with a decimal point are significant (e.g., 2.00 has 3 significant figures).
* Zeros at the end of a number without a decimal point are ambiguous and may or may not be significant (e.g., 200 could have 1, 2, or 3 significant figures).
2. Rounding:
* Addition/Subtraction: The answer should have the same number of decimal places as the number with the fewest decimal places.
* Multiplication/Division: The answer should have the same number of significant figures as the number with the fewest significant figures.
Example:
Let's say you measure a piece of wood to be 12.34 cm long. This has four significant figures, indicating a high level of precision. If you need to round this to two significant figures, you would round it to 12 cm.
The Bottom Line:
The number of significant figures you use in a measurement reflects the precision of your measurement tools and should be consistent throughout calculations to maintain accuracy.
