Always check that your problem is set up completely and that your units cancel correctly before you do the actual calculation. Using dimensional analysis with derived units requires special care. When units are squared or cubed as with area or volume, the conversion factors themselves must also be squared or cubed. Two convenient volume units are the liter, which is equal to a cubic decimeter, and the milliliters, which is equal to a cubic centimeter. The starting and ending units will help guide the setup of the problem.
Next, list any known conversion factors that might be helpful. Once we know the starting units, we can then use the conversion factors to find the answer. Continue to use the conversion factors between the units to set up the rest of the problem. Since the values in these conversion factors are exact numbers, they will not affect the number of significant figures in the answer.
Only the original value 3. Once you have solved the problem, always ask if the answer seems reasonable. Remember, a millimeter is very small and a cubic millimeter is also very small.
If you find that you forgot to cube numbers as well as units, you can setup the problem in an expanded form which is the equivalent to the previous method to cube the numerical values. Allison Soult , Ph. Department of Chemistry, University of Kentucky. Learning Outcomes Convert values among units. Use dimensional analysis to solve problems. Importance of using Correct Conversions In healthcare professions, a calculation error can quite literally have a life or death consequence.
Conversion Factors Many quantities can be expressed in several different ways. Solution This problem requires the conversion from one unit to another so we can use dimensional analysis to solve the problem. Derived Units Using dimensional analysis with derived units requires special care. 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. Converting between metric units is called unit analysis or dimensional analysis.
Unit analysis is a form of proportional reasoning where a given measurement can be multiplied by a known proportion or ratio to give a result having a different unit or dimension. Algebraically, we know that any number multiplied by one will be unchanged. If, however, the number has units, and we multiply it by a ratio containing units, the units in the number will multiply and divide by the units of the ratio, giving the original number remember you are multiplying by one but with different units.
This method can be generalized as: multiply or divide a given number by a known ratio to find your answer. The given number is a numerical quantity with its units. The ratios used are based upon the units and are set up so that the units in the denominator of the ratio match the numerator units of the given and the units in the numerator of the ratio match those in either the next ratio or the final answer. When these are multiplied, the given number will now have the correct units for your answer.
Converting Units with Conversion Factors — YouTube : How to convert units using conversion factors and canceling units. For example, say you were trying to convert 3. You would identify 3. The first step is always to place the given out front of your equation. Then find a ratio that will help you convert the units of grams to atoms. As you probably have already guessed, you need to use a couple of ratios to help you in this problem.
The ratio that 4. Then you set up your ratios so that your units will cancel successfully the same unit must be in the numerator of the equation and also in the denominator of the equation. Lastly, multiply through to get your final answer. As always, your final answer should contain the correct number of sig figs and the correct units.
If you had a sample of a substance with a mass of 0. The given quantity is the mass of 0. To convert a measured quantity to a different unit of measure without changing the relative amount, use a conversion factor. Chemistry, along with other sciences and engineering, makes use of many different units.
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