Recording and Graphing Data

## Recording and Graphing Data

Data is always recorded as accurately and precisely as possible. When a measurement is taken the number of digits recorded should reflect the accuracy of the device used to take the measurement. By convention, you should record all digits you are certain of and then estimate one more.

Most 50 ml graduated cylinders have markings spaced every milliliter while 10 ml graduates have markings every tenth of a milliliter. If we measure a small volume of liquid in a 10 ml graduate, our measurement should be more accurate than if a 50 ml graduate were used. The way in which we record our data should reflect this. Consider the two graduates below.

 We can be certain that the reading is between 26 and 27 ml. We should then estimate one more digit. In this case it is the tenths place. As the bottom of the meniscus appears to be seven tenths of the way from 26 to 27, our reported value should be 26.7 ml. We can be certain that the reading is between 4.7 and 4.8 ml. We should then estimate one more digit. In this case it is the hundredths place. As the bottom of the meniscus appears to be three tenths of the way from 4.7 to 4.8, our reported value should be 4.73 ml.

When reading measurements taken by someone else it is also convention to assume that the uncertain digit (the last one) is +/- 1 of the value shown. Therefore, the volumes measured above should be interpreted as being 26.7 +/- 0.1 ml, and 4.73 +/- 0.01 ml.

The same rules apply to other measurements as well. Consider the rulers below which both measure in centimeters. If the top ruler were used to measure the line, the value should be recorded as 9.28 cm. If the bottom is used, 9.3 cm should be recorded.