Introduction to Measurement

 

Background

            Experimental observations often include measurements of mass, length, volume, temperature and time.  There are two parts to a measurement:

·     Its numerical value

·     The unit of measurement that denotes the scale

 

The numerical value of a laboratory measurement should always be recorded with the proper number of significant figures.  The number of significant figures depends on the instrument or measuring device used and is equal to the digits definitely known from the scale divisions marked on the instrument plus one estimated or “doubtful” digit.  The last, estimated, digit represents the uncertainty in the measurement and indicates the precision of the instrument.

            Measurements made with rulers and graduated cylinders should always be estimated to one place beyond the smallest scale division that is marked.  If the smallest scale on a ruler is centimeters, measurements of length should be estimated to the nearest 0.1cm.  If a ruler is marked in millimeters, readings are estimated to the nearest 0.1mm.  The same reasoning applies to volume measurements made using a graduated cylinder.  A 10mL graduated cylinder has major scale divisions every 1mL and minor scale divisions every 0.1mL.  It is therefore possible to “read” the volume of a liquid in a 10mL graduated cylinder to the nearest 0.01mL.  Three observers might estimate the volume of liquid in a 10mL graduated cylinder as 8.32, 8.30, or 8.33mL.  These are all valid readings.  It would NOT be correct to record this volume of liquid as simply 8.3mL.  Likewise, a reading of 8.325mL would be too precise. 

            Some instruments, such as electronic balances, give a direct reading – there are no obvious or marked scale divisions.  This does NOT mean that there is no uncertainty in electronic balance measurement; it means that the estimation has been carried out internally and the result is being reported digitally.  There is still uncertainty in the last digit.  On an electronic centigram balance, for example, the mass of a rubber stopper might be measured as 5.67g. If three observers measured the mass of the same rubber stopper, they might obtain readings of 5.65, 5.67, and 5.68g.  The uncertainty of an electronic balance measurement is usually one unit in the smallest scale division that is reported – on a centigram balance this would be ± 0.01g.

            Accuracy and precision are two different ways to describe the error associated with measurement.  Accuracy describes how “correct” a measured or calculated value is, that is, how close the measured value is to an actual or accepted value.  The only way to determine the accuracy of an experimental measurement is to compare it to a “true value” – if one is known!  Precision describes the closeness with which several measurements of the same quantity agree.  The precision of a measurement is limited by the uncertainty of the measuring devise.

            Variations among measured results that do not result from carelessness, mistakes, or incorrect procedure are called experimental error.  Experimental error is unavoidable.  The magnitude and sources of experimental error should always be considered when evaluating the results of an experiment. 

 

Experiment Overview

            The purpose of this activity is to have measurements using the metric system, to learn the meaning of significant figures in the measurements, and to compare the accuracy and precision of laboratory measurements. 

 

Pre-lab Question

            How does the concept of significant figures relate to uncertainty in measurement? 

 

 

Procedure

            A data table should be created to organize and collect all relevant information. 

  1. At the front of the room there are three graduated cylinders, each containing a different quantity of water.  Record the capacity and the major and minor scale divisions of each graduated cylinder
  2. Measure the volume of liquid in each cylinder and record the results.  Remember to include the units and the correct number significant figures.
  3. Use tap water to fill a 50mL beaker to the 20mL mark.  Use a pipet to adjust the water level until the bottom of the meniscus is lined up as precisely as possible with the 20mL line.
  4. Pour the water from the beaker into a clean 100mL graduated cylinder.  Measure the volume of liquid in the graduated cylinder and record the results.  Remember to include the unit and correct number of significant figures. 
  5. Pour the water from the 100mL graduated cylinder into a clean 50mL graduated cylinder.  Measure the volume of liquid in the graduated cylinder and record the results.  Remember to include the unit and correct number of significant figures.
  6. Repeat steps three through five two more times for a total of three independent sets of volume measurements.  Record all results.  Dry the beaker and graduated cylinder between trials.

Post Lab Questions

1.      Which graduated cylinder(s) gave the most precise measurement?  Does the number of significant figures allowed for each volume measurement reflect the precision of the graduated cylinders?  Does the diameter of the cylinder have an effect on the accuracy of the measurement?

2.      If you are measuring approximately 8mL of a liquid, what size of graduated cylinder would you look to use?

3.      Why is always a bad idea to use a beaker for volume measurements?