Taking Measurements Reading to Precision

Accuracy Verse Precision We often use the terms accurate and precise to mean the same thing, when in actuality, they have different meanings. When working in the lab, it is important to be both accurate AND precise.

Accuracy Accuracy Accuracy refers to how close a measurement is to an established value. Imagine you are playing darts and your objective is to hit the bull's-eye with three darts. If you come really close to the bull’s-eye on each of your throws, you would be accurate. Accuracy refers to how close a measurement is to an established value. Imagine you are playing darts and your objective is to hit the bull's-eye with three darts. If you come really close to the bull’s-eye on each of your throws, you would be accurate.

This would be an example of an accurate dart players round. Notice that the “hits” are close to the center bull’s-eye, but they are not necessarily close to each other.

Example: Imagine using a tape measure to measure a football field. You know the field is 100 yds long and when you measure it, you find it to be 99.3 yds. Your measurement would be considered accurate.

Precision Precision refers to the repeatability of measurements. Back to the dart analogy. If you throw your darts at the board and all of your darts are grouped very close to one another, you are precise. Notice that I made no reference as to how close the darts were to the bull’s-eye.

These marks would be considered very precise. Notice that the marks are all close to each other, but not to the bull’s-eye.

What would the dartboard look like after a player who is both accurate and precise had a turn?

Relating Accuracy and Precision to Measuring the Lab In lab, we will have to make many measurements using a number of different tools. Each tool should be read to the proper precision in order to be successful in lab. In general, measurements should be made to have one smaller place than the smallest increment on the measuring device.

Determining Increments on Measuring Devices. The first step in determining what the markings of a measuring device represent is to subtract two adjacent numbered marking from each other. In this example, when we subtract 50ml from 60ml, we get 10ml. This means that 10ml of a liquid can fit between the 50ml and 60ml marks on this graduated cylinder.

Determining Increments on Measuring Devices Continued. The next step is to count the number of marks, or increments, between the numbered marks. When doing this, we also count 1 of the numbered marks. For this example, there are 10 marks

Determining Increments on Measuring Devices Continued. The last step is to divide the amount measured between numbered marks by the number of increments between numbered marks. For our example, we have 10mL between 10 marks, so each mark represents 1ml.

Example This ruler has marks every tenth of a centimeter. One place smaller than a tenth of a centimeter is a hundredth of a centimeter

Certain vs. Uncertain Digits The smallest increment on a measuring device is known as the smallest certain digit. This is because there is no estimating involved in determining that number, it is just read from the device. In the example from the previous slide, the smallest certain digit would be one tenth of a centimeter because that is how much space is between each of the smallest increments on the meter stick.

Certain vs. Uncertain Digits Continued The uncertain digit is also called the estimated digit. In the meter stick example, the number that would fall in the 1/100th of cm place would be the estimated digit. All measurement must end with 1, and only 1, estimated or uncertain digit!

Examples: Imagine that the numbers listed on the ruler above represent millimeters. The measurement at letter A would be 0.50mm. The first “0” is a certain digit because we can see that letter A lies before the 1mm mark The “5” tells us that letter A falls at a point between 0.5 and 0.6. It appears that letter A is directly on the 0.5 mark, but we still have to take our measurement to one estimated digit. Since it appears to be directly on the 0.5 mark, we show that to anyone who might look at our data by writing this measurement as 0.50mm

Letter B is a little more tricky. We can tell by the measurement B is between the 1 and the 2 mm mark, so we know the first certain digit is going to be 1 We can also tell that letter B is at least 3 marks in from the 1mm mark, but is not as far as the 4th mark, so the smallest certain digit is 3. Now we have to estimate the last digit. The arrow looks like it is not quite half way between the 3rd and 4th mark, so a reasonable estimate for the last digit would be 4. When we put these digits together, our measurement becomes 1.34mm

Practice! What measurements are represented by letters C, D, E, and F?