Bellringer 9 / 9 / 2009 Rephrase the following quotation in your own words “There is nothing so far removed from us to be beyond our reach, or so far hidden that we cannot discover it.” Rene Descartes

Today’s Lesson Accuracy, Precision, and Significant Figures

Accuracy Accuracy is the degree of closeness of a measured or calculated quantity to its actual (true) value

Precision Precision, also called reproducibility or repeatability, is the degree to which further measurements or calculations show the same or similar results

High Accuracy, but low precision

High precision, but low accuracy

The results of calculations or a measurement can be accurate but not precise, precise but not accurate, neither, or both. A measurement system or computational method is called valid if it is both accurate and precise

Significant Figures A convention used by scientists to indicate a quantity's degree of precision and accuracy

Sig. Figs. Convey The Degree of Precision and Accuracy When recording data, the number of significant figures used depends upon the instrument used to measure the data. When taking a measurement, the last digit we can record is the first digit we must estimate. This will make more sense if we look at the examples below.

We know for certain that the length of the line is more than 4cm but less than 5cm We can estimate it is about half way between 4cm and 5cm, say 4.5cm We had to estimate the.5, so it is the last number we can record. We have two significant figures We would record our measurement as 4.5cm

In this example, we have a ruler marked with finer gradations Since the ruler is more precise, we will have more significant figures We know for sure that the line is between 4.7cm and 4.8cm long We can estimate that it is about mid way between 4.7cm and 4.8cm, so we would record the measurement as 4.75cm Here we have three significant figures

What about situations where the data is given to us?

How to Know What’s Significant All non-zero digits are significant examples 23 has two significant figures 4.5 has two sig figs 235 has 3 sig figs

Zeros are Significant Sometimes When?

Rules for Determining Whether Zeros are Significant Figures 1. Zeros between other nonzero digits are significant Examples 50.3 has three sig figs has five sig figs

Zero Rules cont’d 2. Zeros in front of nonzero digits are not significant Examples has three sig figs has one sig fig

Zero Rules cont’d 3. Zeros that are at the end of a number and to the right of the decimal are significant Examples has four sig figs has seven sig figs

Zero Rules cont’d 4. Zeros at the end of a number but to the left of a decimal may or may not be significant. We will assume they are not significant Examples 1000 has one sig fig 20 has one sig fig

Rules for Calculating with Significant figures Addition or Subtraction: The final answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal Example = which rounds to 103.2

Rules for Calculating cont’d Multiplication or Division: The final answer has the same number of significant figures as the measurement having the smaller number of significant figures Example 123 x 5.35 = which rounds to 658

Rules for Rounding Round Down if: When digit following the last sig fig is a 0,1,2,3,4 Example rounds to 30.2 If last sig fig is an even number and the next digit is a 5 Example becomes 32.2

Rules for Rounding cont’d Round up if: The digit following the last sig fig is a 6, 7, 8, 9 Example becomes 22.5 The last sig fig is an odd number and the next digit is a 5 Example becomes 54.8