The following lesson is one lecture in a series of Chemistry Programs developed by Professor Larry Byrd Department of Chemistry Western Kentucky University

Excellent Assistance has been provided by: Dr. Robert Wyatt Ms. Elizabeth Romero Ms. Kathy Barnes

PART 1 Significant Figures

I. Uncertainty in Measurements The only kind of physical quantity that can be measured with complete accuracy would occur in simple counting operations, such as I have 25 dollars and 13 cents, or I see two dogs. In chemistry, as in other sciences, quantities such as length, mass, volume and density of objects often have many different values.

Accuracy & Precision ACCURACY and PRECISION are terms that are often used in regard to a measured quantity. These two terms have different meanings and if we wish to become competent in making measurements and in interpreting data, we must also understand their differences.

ACCURACY is concerned with how close a measurement comes to the accepted or true value. PRECISION is the agreement between the numerical values of two or more measurements that have been made in the same way However, precise measurements are not always accurate. The following example will illustrate the distinction between accuracy and precision: Accuracy & Precision

Mr. Jones waited anxiously as Mrs. Jones opened her valentine present. It was one of the new bathroom scales that displays your weight on a lighted scale and at the same time, in a spoken voice, it will tells you your weight. As Mrs. Jones stepped upon the scale, Mr. Jones is telling her how the salesman demonstrated the scale to him. The salesman showed how accurate the scale was by having Mr. Jones weigh himself three times and observed that all the readings were within one-tenth (0.1) of a pound. Accuracy vs. Precision

Mrs. Jones was very pleased with her present, especially since the scale announced that her weight was pounds. Mrs. Jones said that the last time she weighed herself on their old bathroom scales that her weight was over 130 pounds, but she told Mr. Jones that she knew that was wrong because she had never weighed that much. That night at dinner, Mrs. Jones cooked Mr. Jones' favorite dishes. Accuracy vs. Precision

The next day Mrs. Jones was in the bathroom getting ready for her yearly physical at her doctor's office. She decided that she would check her weight before she left so she could compare it to the doctor's scales. She weighed herself three more times. The values were 125.7, 125.6, and pounds. Mrs. Jones was confident that her weight was probably pounds or pounds. Accuracy vs. Precision

At the doctor's office, the nurse had Mrs. Jones step upon their weight scales. The nurse told Mrs. Jones that her weight was pounds. Mrs. Jones quickly replied that could not be correct and that their scale must be faulty. The nurse explained that the doctor's scale was constantly compared to standard weights so that the scale was always accurate to one-tenth of a pound. Accuracy vs. Precision

After the nurse left the room, Mrs. Jones was sure the nurse misread her weight. She reweighed two more times. The last two values were and pounds. Thus, Mrs. Jones' true weight (accurate weight) is close to pounds and not pounds as her bathroom scales would suggest. Accuracy vs. Precision

When the doctor came in and looked at her chart, he reminded her that she had never weighed that much and should lose 10 pounds. As Mrs. Jones sat there half-way listening to the doctor, she was thinking about what she was going to do with those new bathroom scales when she got home. I also have a strong feeling that the man that bought that "very accurate" gift may not have his favorite dishes at dinner for a long time! Accuracy vs. Precision

Observe, that PRECISION involves only the agreement between the numerical values of two or more measurements that are made under the same conditions. At home, Mrs. Jones' new scale was very precise. However, as Mrs. Jones learned at the doctor's office, values obtained in measurements may be precise but they may not be accurate Accurate vs. Precision

ACCURACY means the nearness of a measurement to the true or accepted value. For measurements to be considered to be accurate, we must have well trained people using equipment that is carefully used and constantly calibrated against very accurate standards. In the case of Mrs. Jones, the scale in the doctor's office can be considered to be very accurate since it meets the above requirements. Accuracy vs. Precision

Her three readings in the office were 132.4, and pounds. These values show a high degree of precision (close to each other!) and they are also accurate. Normally, repeated measurements that show good precision are an indication of high accuracy. However, as Mrs. Jones found out, this is not always true

Whenever we are using data from some other person's experiment, we must assume that they have made a major effort to be sure that all reported values are accurate. If this is not the case, we are wasting our time using that data.