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Units of measurement

Measuring devices are used for many purposes: rulers measure length, thermometers measure temperature, and scales measure weight. What they all have in common is the fact that the results obtained are in numbers: 10 centimeters, 35 degrees, or 100 grams. Some things cannot be measured accurately, but they can be assessed and compared. Examples are love, anger, even taste and smell. We love our parents more than our schoolteachers; ice cream tastes better than spinach or onion. Assessment and comparison are a type of preparatory stage to proper measurement. If we look at two children standing side by side we can tell which is taller. If we touch two objects we can tell which is warmer. But such assessments and comparisons cannot tell us accurate height or temperature. Furthermore, if the children are not standing together, or if we do not touch the two objects at the same time, it will be difficult to compare them. Measuring devices tell us precisely what we want to know without being dependent on other objects for comparison. But in fact, nearly every measuring device and measuring process is based on comparison, not comparison between two objects but comparison with a standard size. A ruler measures length by comparison with a standard unit of measurement (for example, a centimeter), by ‘counting’ how many times the unit of measurement ‘goes into’ the length being measured. A thermometer ‘counts’ how many degrees ‘go into’ body temperature, and scales ‘count’ how many units of weight (for example, grams or kilograms) ‘go into’ body weight.

Basic and fundamental units of measurement include:
  • Length, measured in millimeters, centimeters, meters, kilometers – note that they are all related to the meter (millimeter = one thousandth of a meter, centimeter = one hundredth of a meter, kilometer = one thousand meters…).
  • Weight or force, measured in milligrams (one thousandth of a gram), grams, kilograms (one thousand grams).
  • Time (second, minute, hour…)

Some units of measurement are combinations of others.

For example, area is measured in units of square centimeters, square meters, or square kilometers. In other words, a unit of area that is the square of its length in centimeters, meters, or kilometers.

Volume is measured in liters, cubic meters, or cubic centimeters. In other words, the volume equals the volume of a cube whose length is a meter or centimeter.

Flow rate is the amount (volume) of material passed through a given time, for example, one liter per second.

Methods of measurement

Measuring devices sometimes measure the measured units themselves: for example, on a carpenter’s ruler we can actually see how many centimeters ‘go into’ the length of the object, and a measuring cup into which liquid is poured ‘counts’ the volume of liquid inside. But some devices measure other amounts, from which we can calculate the amount we want to measure. A simple scale or dynamometer is based on a spring (or even an elastic band) that grows longer as more force is exerted. By measuring the length we can determine how much force was exerted.

Reproducibility and reliability

The most important aspect of measuring devices is their ability to repeat and reproduce results. In other words, each time we measure the same thing, we must obtain the same result. If we attach a 100 gram weight to a spring scale it must extend the same distance each time we measure it, morning or evening, hot or cold. The same result should be obtained even if we start with 50 grams and then add another 50 grams, or if we start with 200 grams and then deduct 100 grams. The reading must remain constant the moment we hang the weight and two hours later. Unfortunately no measuring device is capable of reproducing results with 100% accuracy. There will always be slight differences between readings. Sometimes they are caused by temperature, by obsolescence, or simply because the device is inaccurate or it is being used incorrectly. Weigh yourself five or ten times on your scale at home and see whether you get the same result every time. Take your temperature ten times and see whether all the readings are identical. If the differences are very slight, it doesn’t really matter. But bear in mind that there are slight inaccuracies in every measurement and we must decide for ourselves how accurate our measurement needs to be. For the most part, accuracy to one tenth or one half percent (or even one percent) is sufficient. If you measure the width of your notebook, for example, you will do so in centimeters or millimeters. Obviously a difference of one tenth or one hundredth of a millimeter is not important. The same applies when you measure your weight in kilograms, at most it will be accurate to within half a kilogram. When measuring the distance between cities we do so in units of kilometers, and a difference of tens or even hundreds of meters hardly matters.

Sometimes the inability to reproduce results lies with the measurand rather than the measuring device (measuring blood pressure, for example). In this case it is customary to repeat the measurement several times and calculate the average reading. This method of obtaining an average from a large number of readings is also helpful in other situations, when measuring something very small, for example. It is impossible to measure the thickness of a sheet of paper with a ruler, so we measure the thickness of a sheaf of 100 or 200 sheets and then divide the result by 100 (or 200). We have thus calculated the average of 100 or 200 measurements, where each one on its own would have been extremely inaccurate.

Monovalence – one size – one number

The second important aspect of measuring devices is that its reading should only relate to one quality of the amount being measured. In other words, the spring scale will lengthen by one centimeter only when a 100 gram weight is suspended from it. If a different weight is suspended – 200 grams, for example – it will lengthen by 2 centimeters. A 300 gram weight will give a 3 centimeter reading, and so on. However, there are several exceptions to this rule. With cyclic measurements such as time, for example, the value repeats itself (this is what is meant by cyclic measurement – it is a measurement that repeats itself) and so does the reading. The hands of a clock show the hour 12 times a day, and furthermore the minute hand returns to the same place every hour. When the minute hand is pointing to the three we know the time is “some” hour plus 15 minutes (or “some” hour and a quarter). The hour hand tells us what hour it is and we can easily tell whether it is day or night.

Other exceptions to the rule of the size being measured and the reading displayed by the measuring device are the boundaries of the amount being measured. Each measuring device is formulated and capable of measuring a particular amount. Anything beyond this amount will not be measured, and the readings will be meaningless. A thermometer intended to measure body temperature displays the numbers between 35 and 42 degrees. Anything below 35 degrees on the mercury column will always read 35 degrees, while anything above 42 degrees will read 42 degrees. The principle of monovalence does not apply and it is clear that we cannot measure temperatures that are too high or too low with this thermometer. As a rule there is a connection between the maximum and minimum the measuring device is capable of measuring. Extremely sensitive instruments that are capable of measuring very small amounts are incapable of measuring very large amounts. If we bring down the lower gauge, we must bring down the upper gauge as well. The opposite also holds true. Instruments that are capable of measuring very large amounts are incapable of discerning differences between small amounts. A scale designed to weigh trucks and other objects weighing thousands of kilograms is incapable of distinguishing between one gram and 10 grams, both of which will register zero on the pointer of the scale.
Date Created: 05/05/13
Date Updated: 05/05/13