How to compare values: a step-by-step instruction. What values can be compared: examples

From the earliest days people were seriously interested in the question of how it is most convenient to compare values expressed in different values. And it's not just a matter of natural curiosity. The man of the oldest terrestrial civilizations gave this rather difficult matter a purely applied significance. Correctly measure the land, determine the weight of the product on the market, calculate the necessary ratio of goods at barter, determine the correct rate of grapes for the collection of wine - that's just a small part of the tasks that often pop up in the already hard life of our ancestors. Therefore, poorly educated and illiterate people, if necessary, compare the values followed the advice to their more experienced comrades, and they often took appropriate bribes for such a service, and quite good, by the way.

What can you compare

In our time, this occupation also plays a significant role in the process of studying the exact sciences. Everyone, of course, knows that it is necessary to compare the uniform quantities, that is, apples - with apples, and beets - with beets. Nobody will ever think of expressing degrees Celsius in kilometers or kilograms in decibels, but we know the length of the boa constrictor in parrots since childhood (for those who do not remember: in one boa, there are 38 parrots). Although the parrots are also different, and in fact the length of the boa constrictor will vary depending on the parish subspecies, but these are the details in which we will try to figure it out.

Dimensions

When the job says: "Compare the values of the quantities", these same quantities must be brought to the same denominator, that is, expressed in the same values for convenience of comparison. It is clear that to compare the value expressed in kilograms, with the value expressed in centners or tons, for many of us it will not be difficult. However, there are homogeneous quantities that can be expressed in different dimensions and, moreover, in different measurement systems. Try, for example, to compare the kinematic viscosity values and determine which of the liquids is more viscous in centistokes and square meters per second. Does not work? And it will not work out. To do this, both values must be reflected in the same quantities, and by numerical value, determine which of them exceeds the opponent.

Measurement system

In order to understand what quantities can be compared, let us try to recall the existing measurement systems. To optimize and accelerate settlement processes in 1875, seventeen countries (including Russia, the United States, Germany, etc.) signed a metric convention and defined a metric system of measures. For the development and consolidation of the standards of the meter and kilogram, the International Committee for Weights and Measures was established, and in Paris, the International Bureau of Weights and Measures is equipped. This system eventually evolved into the International System of Units, SI. At present, this system has been adopted by the majority of countries in the field of technical calculations, including those where traditional physical quantities are used in everyday life (for example, the USA and England).

GHS

However, in parallel with the generally accepted standard of standards, another, less convenient system of GHS (centimeter-gram-second) developed. It was proposed in 1832 by the German physicist Gauss, and in 1874 was modernized by Maxwell and Thompson, mainly in the field of electrodynamics. In 1889, the more convenient ISS system (meter-kilogram-second) was proposed. Comparison of objects in terms of the standard values of meter and kilogram for engineers is much more convenient than using their derivatives (centi-, milli-, deci-etc.). However, this concept also did not find a mass response in the hearts of those for whom it was intended. Throughout the world, the metric system of measures was actively developed and used , so the calculations in the GHS were less and less, and after 1960, with the introduction of the SI system, the GHS was completely out of use altogether. Currently, the GHS is actually used in practice only in calculations in theoretical mechanics and astrophysics, and then because of the simpler form of recording the laws of electromagnetism.

Step-by-step instruction

Let us examine in detail an example. Let's say the problem sounds like this: "Compare the values of 25 tons and 19570 kg." Which of the values is greater? " What needs to be done first, first, is to determine in which quantities we have values. So, the first value is given in tons, and the second in kilograms. In the second step, we check whether the authors of the problem are trying to mislead us, trying to force us to compare different quantities. There are also such tasks-traps, especially in fast tests, where the answer to each question is 20-30 seconds. As we see, the values are uniform: both in kilograms and in tons we measure the mass and weight of the body, so the second check is passed with a positive result. The third step, we translate kilograms in tons or, conversely, tons - in kilograms for convenience of comparison. In the first variant, 25 and 19.57 tons are obtained, and in the second variant: 25,000 and 19,570 kilograms. And now you can compare the values of these values with calm soul. As can be clearly seen, the first value (25 tons) in both cases is greater than the second (19,570 kg).

Traps

As mentioned above, modern tests contain so many deceptive tasks. This is not necessarily the tasks we have analyzed, the trap may turn out to be a rather innocuous question, especially, where a completely logical answer arises. However, insidiousness, as a rule, lies in the details or in a small nuance, which the compilers of the task try to disguise in every possible way. For example, instead of the problem already familiar to you on disassembled questions with the statement of the question: "Compare the values where possible", the compilers of the test can simply ask you to compare the indicated quantities, and the quantities themselves should be strikingly similar to each other. For example, kg * m / s ² and m / s ² . In the first case, this is the force acting on the object (newtons), and in the second - the acceleration of the body, or m / s ² and m / s, where you are asked to compare acceleration with the speed of the body, that is, completely different quantities.

Complex comparisons

However, very often two assignments are given in tasks, expressed not only in different units of measurement and in different systems of calculus, but also different from each other in the specificity of the physical meaning. For example, the statement of the problem says: "Compare the values of the dynamic and kinematic viscosities and determine which fluid is more viscous." In this case, the kinematic viscosity values are indicated in SI units, that is, in m ² / s, and the dynamic value in SGS, that is, in poises. What should I do in this case?

To solve such problems, you can use the above instructions with a little addition. Determine which of the systems will work: let it be a SI system, generally accepted among engineers. We also check the second step, but is not it a trap? But in this example, too, everything is clean. We compare two fluids by the parameter of internal friction (viscosity), so both quantities are uniform. The third step is to translate the dynamic viscosity from poise to pascal-second, that is, to the conventional units of the SI system. Next, we translate the kinematic viscosity into dynamic viscosity, multiplying it by the corresponding value of the liquid density (tabulated value), and we compare the results obtained.

Outside the system

There are also extrasystem units of measurement, that is, units that are not included in the SI, but according to the results of decisions to convene general conferences on measures and weights (GKVM), permissible for joint use with SI. It is possible to compare such quantities among themselves only if they are reduced to the general form in the SI standard. Such units as minute, hour, day, liter, electron-volts, node, hectare, bar, angstrom and many others belong to the off-system unit.