Using Scientific Measurements

Accuracy and Precision Accuracy is the closeness of measurements to the correct or accepted value of the quantity measured. Precision is the closeness of a set of measurements of the same quantity made in the same way (close to one another, but not necessarily close to accepted value.

How are accuracy and precision related?

How is accuracy and precision measured? Percent error is calculated by subtracting the accepted value from the experimental value, dividing the difference by the accepted value, and then multiplying by 100.

A student measures the mass and volume of Sample Problem: A student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percentage error of the student’s measurement? 1.40 g/mL - 1.30 g/mL x 100 = 7.7% % Error = 1.30 g/mL Notice that the student’s percentage error is a positive number.

What does a positive or negative percentage error mean? (-) Percent Error – accepted value is greater than experimental value (+) Percent Error – accepted value is less than experimental value In the sample problem the student’s experimental value was 1.40 g/mL and the accepted value was 1.30 g/mL. His percentage error was positive.

Why do (should) we care about percentage error? Error or uncertainty always exists in any measurement. The skill of the measurer or instrument may affect the outcome.

Significant Figures Significant Figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated. The term “significant” does not mean certain.

Yes!!!!! What value should be recorded for the length of this nail? 6. What digit should be recorded first? Second? Third? Yes!!!!! 6. 3 5 cm Do we need to add a unit?

Rules for Determining Significant Zeros Zeros appearing between nonzero digits are significant. Example: 1001 has 4 significant figures. Zeros appearing in front of all nonzero digits are not significant. Example: 0.004 has 1 significant figure. Zeros at the end of a number and to the right of the decimal point are significant. Example: 0.004500 has 4 significant figures.

Zeros at the end of a number but to the left of a decimal point may or may not be significant. If a zero has not been measured or estimated but is just the placeholder, it is not significant. A decimal point placed after zeros indicated that they are significant. Example: 500 has 1 significant figure 500. has 3 significant figures 500.0 has 4 significant figures

Addition or Subtraction with Significant Figures When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point. 2 decimal places Example: 2.35 cm + 1.359 cm 3 decimal places 3.709 cm answer can only have 2 decimal places 3.71 cm

Multiplication and Division with Significant Figures For multiplication or division, the answer can have no more significant figures than are in the measurement with the fewest number of significant figures. Example: 2.35 cm x 4.1456 cm = 9.74216 cm2 9.74 cm2 3 significant figures 5 significant figures Round to 3 significant figures