Converting units using dimensional analysis makes working with large and small measurements more convenient. For most quantities, a unit is absolutely necessary to communicate values of that physical quantity. Imagine you need to buy some rope to tie something onto the roof of a car. How would you tell the salesperson how much rope you need without using some unit of measurement?
However, not all quantities require a unit of their own. Using physical laws, units of quantities can be expressed as combinations of units of other quantities.
Therefore, only a small set of units is required. These units are called base units , and other units are derived units. Derived units are a matter of convenience, as they can be expressed in terms of basic units. Different systems of units are based on different choices of base units.
There are seven SI base units, and all other SI units can be derived from these base units. The base units of SI are actually not the smallest set possible; smaller sets have been defined. For example, there are unit sets in which the electric and magnetic field have the same unit. This is based on physical laws that show that electric and magnetic fields are actually different manifestations of the same phenomenon. Derived units are based on units from the SI system of units.
For example, volume is a derived unit because volume is based on length. To calculate the volume of something, you multiply the width x length x height, all in meters. Therefore, the derived unit for volume is m 3. Here is a list of some commonly derived units:. Sometimes, it is necessary to deal with measurements that are very small as in the size of an atom or very large as in numbers of atoms. In these cases, it is often necessary to convert between units of metric measurement. For example, a mass measured in grams may be more convenient to work with if it was expressed in mg 10 —3 g.
That is, he replaced the picture above, which is more hemispherical, with:. Here, indicates mass, indicates length, and indicates time. We do care that our base units are irreducible.
His next step was to assume a functional relationship of a particular form between his four quantities. He imagined that the blast radius could be determined if he knew the energy released in the blast, the density of the surrounding air, and the time elapsed since the explosion. So, he wrote the radius as a product of powers of these three quantities.
This is the key step in dimensional analysis. The powers, , , and are not yet known. But, Taylor did know that his assumed functional form had to be dimensionally consistent. The correct answer is This would have been true if the difference in weight was 8 dag, not 80 dag. The first boxer is 80 dag heavier , not lighter than his opponent. Checking your Conversions. Sometimes it is a good idea to check your conversions using a second method. This usually helps you catch any errors that you may make, such as using the wrong unit fractions or moving the decimal point the wrong way.
A two-liter bottle contains 87 centiliters of oil and 4. How much more liquid is needed to fill the bottle? You are looking for the amount of liquid needed to fill the bottle.
Convert both measurements to liters and then solve the problem. Convert 4. Subtract to find how much more liquid is needed to fill the bottle. The amount of liquid needed to fill the bottle is 0. On the chart, l is two places to the left of cl. Move the decimal point two places to the left in 87 cl. To convert from one unit to another within the metric system usually means moving a decimal point. If you can remember what the prefixes mean, you can convert within the metric system relatively easily by simply multiplying or dividing the number by the value of the prefix.
The song includes an explanation of the following prefixes: kilo, hecto, deca, deci, centi, and milli. It is possible dividing the value of length by Also, check centimeter to foot calculator. By multiplying the value of length by 0. Begin typing your search term above and press enter to search.
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