1.7: The Reliability of a Measurement

significant figures

In any reported measurement, the non–place-holding digits (those that are not simply marking the decimal place) that indicate the precision of the measured quantity.

4 Significant Figure Rules

1. All nonzero digits are significant

2. Interior zeros (between 2 nonzero digits) are significant

3. Leading zeros (zeros to the left of the first nonzero) are not significant. They only serve to locate the decimal point

4. Trailing zeros…

   1. after a decimal point are always significant

   2. before a decimal point (and after a nonzero number) are always significant

rules for determining dig figs in calculations

1. Multiplication or Division: The result has the same amount as the factor with the fewest sig figs.

2. Addition or Subtraction: The result has the same number of digits after the decimal place as the quantity with the fewest decimal places.

3. When rounding, round down if the last digit is four or less, round up if the last digit is five or more

4. round only the final answer, not intermediate steps

accuracy

how close the measured value is to the actual value

precision

how close a series of measurements are to one another, how reproducible they are