Measurement, Accuracy and Errors

Medir es comparar una magnitud desconocida con un patrón que tomamos como referencia y que llamamos unidad. El resultado de la medida es el producto de un número real por la unidad de referencia.

Hay unidades fundamentales que se eligen arbitrariamente y derivadas que se definen a partir de las fundamentales.

El sistema internacional de unidades (SI) se elabora por la Conferencia General de Pesas y Medidas, que se reune para corregirlo cada cuatro años.

El SI consta de 7 unidades fundamentales, las unidades 2 suplementarias y las unidades derivadas.

In no subject does measurement play as important a role as in science. Real science cannot exist without measurement. According to Lord Kelvin, one of the greatest scientists, unless you can measure what you are speaking about and express it in numbers you have not started 'Exact Science'.

Thus there are two aspects regarding measurements. One is actual MEASUREMENT of objects or happenings and the second is expressing that in terms of NUMBERS.

Physics is an exact science. It deals with accurate measurements. But the question comes up 'How much accuracy do we need to make our measurements accurate?'

The answer depends upon the purpose for which measurements are made. To know exact time we take to reach the school we may need to know the number of minutes we take to reach the school. But Olympic records need timings in fractions of seconds! For us the year is equal to 365 or 365.25 days. And it is acceptable. But ask an astronomer. He will say that it is equal to 365.242195 days! But apart from such astronomers, for whom is such accuracy important?

Everything that we use in our daily life is ultimately governed by principles of physics. All gadgets we use everyday at home, bicycles and cars, all different types of machinery and instruments, work on principles of physics. Hence to understand even the elementary working of these things, the study of physics is essential.

For understanding the relationships between matter and energy, measuring them is very essential. There are thousands and thousands of different things around us. There are different kinds of forces around us and there are different kinds of energies that we come across every day. Thus there would be millions and millions of physical quantities and energies that could be measured. Yet you would be surprised to know that there are only six basic units from which all other units are derived. These basic units are the units of length, mass, time, electric current, temperature and luminous intensity. Out of these only three fundamental or basic units of measurements are used in mechanics.

These are the units length, mass and time. All the measurements in physics are related to these three fundamental units. All other units of measurements can be derived from these three fundamental units.

While discussing these units of measurement we must be clear about two terms - unit and measure number. For example, when we say that the length of a line is five centimeters, the unit we have chosen is centimeter and the measure number is five as the line is five times the unit length.

Quantitative vs. Qualitative

Most experiments in physics require the observations made to be quantitative rather than qualitative. If observations are only descriptive or qualitative, they are likely to be imprecise and could cause disagreements between experimenters. For example, scientists cannot merely say that an object is large or small. Instead they have to specify its size as a quantity, that is, with a number and using a standard unit such as kilogram. This is called a quantitative observation.

As science advanced through the centuries, the importance of accurate and uniform measurements was realized all over the world. In order to enable scientists working in different parts of the world to compare their measurements, a need for certain basic unit of measurement was felt and hence later a basic unit was defined.

Unit is a standard for comparison. In earlier times the measurement of quantity of things was quite arbitrary. In many cases it was related to the dimension of different parts of the human body. These parts were chosen as "units" to measure these quantities. For example, for measuring length, distance between the nose and the fingers or outstretched hand was used as a unit. Can you imagine the confusion caused when different countries used different units or measures! This also caused a lot of inconvenience.

Estimation

It is easy to measure the length of your page but if you are asked to find the height of a high rise building how would you do it? It is of course possible to do that by going to the terrace of the building, hanging a rope… etc. Not very convenient!

On the other hand one can estimate approximate height of a floor and then do some simple arithmetic to arrive at a figure which, though not accurate from the point of view of an architect, may serve our purpose. Thus even if accurate measurement is necessary it is always advisable to estimate. This would help; you to avoid silly mistakes that frequently take place while calculating.

For better estimations, specially for large numbers, comparison is easier to make. For example in the above calculations it would be easier to compare the height of the high rise building in terms of a building with two or three storeys.

Approximation

In measurements approximation also plays an important role. In day to day practice we always use approximation. You must have heard people saying "It is approximately five minutes walk from the station" or "Both of them are more or less of the same height" etc. Approximations also play an important role in science. To give you some idea about the size of an atom your chemistry teacher would say, "In a centimetre, there might be approximately 100 million atoms lying side by side!"

Accuracy

It is the smallest reading that can be accurately measured while using an instrument or a device. For example the least count of various measuring devices are listed below:

Significant Figures along with Examples

These express the degree of accuracy of measurements. It is a statement which gives number of digits up to which we are sure about their accuracy. It gives the degree of accuracy or precision made with the instrument. In practical life we depend only on approximate measurements. We ignore small measurements when we are computing large measurements. For example, we may measure the length of a wall as 10 meters and 57 centimeters or 10.57 meters. The actual length of the wall is between 10 meters 57.5 cm and 10 meters 56.5 cm. Now we can say that the length 10.57 meters is correct up to four significant figures.

Measuring instruments have a limit upto which measurements can be made, called as the least count of the instrument. Errors are seen when measuring through various instruments. For e.g., accuracy of the temperature measured by thermometer depends on the thermometer and the measuring person. If the temperature of hot water is 99.9^o C and if the thermometer gives exactly 99.9^o C then the measured value is accurate, or else it is an error.

Accuracy depends on

• The range of instruments used
• Least count
• Sensitivity of the instrument
• hysteresis
• Quick response of the instrument to the physical quantity to be measured