Measurement conversion problems, solving

There are a variety of problem-solving strategies that you will use as you prepare for and take the AP test. Dimensional analysis, sometimes known as the factor label method, is one of the most important of the techniques for you to master. Dimensional analysis is a problem-solving technique that relies on the use of conversion factors to change measurements from one unit to another. It is a very powerful technique but requires careful attention during setup. The conversion factors that are used are equalities between one unit and an equivalent amount of some other unit. In financial terms, we can say that 100 pennies is equal to 1 dollar. While the units of measure are different (pennies and dollars) and the numbers are different (100 and 1), each represents the same amount of money. Therefore, the two are equal. Let s use an example that is more aligned with science. We also know that 100 centimeters are equal to 1 meter. If we express this as an equation, we would write ... 

The conversion between the three principal measures of quantity of matter— the number of grams (mass), the number of moles, and the number of individual particles (atoms, ions, or molecules)—is essential to the art of problem solving in chemistry. Their interrelationship is depicted in Figure 5.2. 

Three systems for measuring temperature are widely used the Celsius scale, the Kelvin scale, and the Fahrenheit scale. The first two temperature systems are used in the physical sciences, and the third is used in many of the engineering sciences. Our purpose here is to define the three temperature scales and show how conversions from one scale to another can be performed. Although these conversions can be carried out routinely on most calculators, we will consider the process in some detail here to illustrate methods of problem solving. 

Measurements of Length, Volume, and Mass Uncertainty in Measurement Significant Figures Problem Solving and Dimensional Analysis Temperature Conversions ... 

Appendix C Units of Measure, Unit Conversion, and Problem Solving... 

A measured quantity consists of a number and a unit. Conversion factors are used to express a quantity in different units and are constructed as a ratb of equivalent quantities. The problem-solving approach used in this text usually has four parts (1) devise a plan for the solution, (2) put the plan into effect in the calculatbns, (3) check to see if the answer makes sense, and (4) practice with similar problems. 

This book provides a handy and convenient source of formulas, conversion factors and constants for students and professionals in engineering, chemistry, mathematics and physics. Section 1 covers the fundamental tools of mathematics needed in all areas of the physical sciences. Section 2 summarizes the SI system (International System of Units of measurement), lists conversion factors and gives precise values of fundamental constants. Sections 3 and 4 review the basic terms of spectroscopy, atomic structure and wave mechanics. These sections serve as a guide to the interpretation of modem literature. Section 5 is a resource for work in the laboratory, listing data and formulas needed in connection with frequently used equipment such as vacuum systems and electronic devices. Material constants and other data are listed for information and as an aid for estimates or problem solving. 

Chapter 2. Chemistry and Measurements, looks at measurement and emphasizes the need to understand numerical relationships of the metric system. Significant numbers are discussed in the determination of final answers. Prefixes from the metric system are used to write equalities and conversion factors for problem-solving strategies. Density is discussed and used as a conversion factor. 

Most measurements in chemistry are made in SI units. Sometimes we must convert between SI units, as when converting kilometers to meters. At other times we must convert measurements expressed in non-Sl units into SI units, or from SI units into non-Sl units. In all these cases, we can use a conversion-factor or a series of conversion factors in a scheme called a conversion pathway. Later in this chapter, we will apply conversion pathways in a method of problem solving known as dimensional analysis. The method itself is described in some detail in Appendix A. 

The most common continuous emulsion polymerization systems require isothermal reaction conditions and provide for conversion control through manipulation of initiator feed rates. Typically, as shown in Figure 1, flow rates of monomer, water, and emulsifier solutions into the first reactor of the series are controlled at levels prescribed by the particular recipe being made and reaction temperature is controlled by changing the temperature of the coolant in the reactor jacket. Manipulation of the initiator feed rate to the reactor is then used to control reaction rate and, subsequently, exit conversion. An aspect of this control strategy which has not been considered in the literature is the complication presented by the apparent dead-time which exists between the point of addition of initiator and the point where conversion is measured. In many systems this dead-time is of the order of several hours, presenting a problem which conventional control systems are incapable of solving. This apparent dead-time often encountered in initiation of polymerization. 

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