Conversion factor choosing

From your list of six conversion factors, choose the one that has the same units in the denominator as does the given so that the two units will cancel. 

If the remaining units are not the units in the answer, you will need another conversion factor. To choose this conversion factor, look for one with units in the denominator that are the same as the remaining units. Cancel all units that will cancel. If the remaining units are not in the answer, repeat this step. 

Choose a conversion factor that has in its denominator the same units as those accompanying the given number. 

Choose the Conversion Factor That Cancels the Given Units... 

Choose the conversion factor that cancels units of moles and gives an answer in number of atoms. 

Step 2. Insert the required conversion factors to change between units. The conversion factors will be in fraction form, and they will be orientated in such a way that we can cross-cancel the units that we don t want and keep the units that we do want. In this example, we will need either 2 or 3 conversion factors, depending on how you choose to solve it. If you convert inches to yards directly, you will only need 2 conversion factors. For the sake of clarity, I will use two steps to convert inches to yards and will use a total of 3 conversion factors. 

Note that the units in a unit analysis setup cancel just like variables in an algebraic equation. Therefore, when we want to convert tsp to mL, we choose the ratio that has tsp on the bottom to cancel the tsp unit in our original value and leave us with the desired unit of mL. If you have used correct conversion factors, and if your units cancel to yield the desired unit or units, you can be confident that you will arrive at the correct answer. 

There is a lesson here Choose or develop the most efficient conversion factor to solve the problem. If you re converting grams to atoms, find the equality that relates grams and atoms for the conversion factor. If it s mole to atoms, find the connection between mole and atoms. Use the units g Fe, mole Fe, and atoms Fe to guide the correct use of the conversion factor. 

Since this is a doUar-to-penny conversion, we choose the unit factor that has the unit dollar in the denominator (to cancel the dollars in 2.46 dollars) and write... 

The calculation is based on choosing the appropriate conversion factor. The relationship... 

In our example, we want to convert the distance in miles to the equivalent distance in feet. Therefore, we choose the conversion factor with units of feet in the numerator, because it cancels units of miles and gives units of feet ... 

Solution Converting the known length from centimeters to inches The equivalent quantities alongside the roadmap arrow are the ones needed to construct the conversion factor. We choose 1 in/2.54 cm, rather than the inverse, because it gives an answer in inches ... 

Choosing Conversion Factors Eariier in this chapter we considered a pin that measured 2.85 cm in iength. What is the iength of the pin in inches We can represent this probiem as... 

We choose a conversion factor that cancels the units we want to eliminate and leaves the units we want in the result. 

Step 2 Choose the appropriate conversion factor by looking at the... 

How can you decide which conversion factor to choose in a problem ... 

What is an equivalence statement How many conversion factors can be created from one equivalence statement Choose an equivalence statement from Table 5.7, and write all the possible conversion factors from it. 

Then choose the conversion factor that, when multiplied by the known quantity, results in the desired unit. When set up correctly, all units cancel except those required for the answer. 

To solve the problem, you need to know how the unknown moles of hydrogen are related to the known moles of potassium. In Section 11.1, you learned to derive mole ratios from the balanced chemical equation. Mole ratios are used as conversion factors to convert the known number of moles of one substance to the unknown number of moles of another substance in the same reaction. Several mole ratios can be written from the equation, but how do you choose the correct one ... 

Step 2 Choose the appropriate conversion factor by looking at the direction of the required change (make sure the unwanted units cancel). 

Analyze In each case we are given the pressure in one unit and asked to convert it to another unit. Our task, therefore, is to choose the appropriate conversion factors. 

The cancellation of units provides the basis for choosing which conversion factor is needed It is always the one that allows the unit being converted to be canceled and leaves the new unit uncanceled. 

We choose the conversion factor that cancels the unit inches and produces the desired unit, centimeters. Note that the result is expressed in four significant figures because 2.54 is an exact number. 

Because we are converting m to cm, we choose the conversion factor that has meters in the denominator,... 

We pick two points at random, for comparison - 900 °C, 5000 bars, and 100 °C, 100 bars, and choose values from lAPS-84 for comparison with supcrt92. Also included are the more recent values from lAPWS-95, to show the differences from IAPS-84. Conversion factors used are 4.1868 J/cal and 18.015 268 for the molar mass of water. 

A measurement or quantity given in one kind of unit can be converted to any other kind of unit having the same dimension. To convert from one kind of unit to another, the original quantity or measurement is multiplied or divided by a conversion factor. The key to success lies in choosing the correct conversion factor. This general method of calculation is illustrated in the following examples. 

The question of which units to use has been resolved (in many countries) by the adoption of the International System of Units—SI Units. While there is a trend toward the use of SI units in the U.S., its full acceptance will probably take many years. A problem therefore arises, in a multi-author book reviewing the literature, as to what system of units to use. Choosing the SI system would require extensive conversion of original data (often only to be reconverted by the reader into more familiar units). The decision was therefore taken to leave all quantities reported in the units used in the original text this necessarily means that a mixture of units is to be found in the following chapters. To help in the conversion from one system to another, a guide to the use of SI units will be found in Appendix II, together with recommended conversion factors. 

Density The density of substances is an important consideration in choosing materials from which to make things. Airplanes, for example, are made of low-density materials, while bridges are made of higher-density materials. Density is important as a conversion factor between mass and volume and vice versa. 

Choosing the Correct Conversion Factor It is easier to convert if you first decide whether the answer expressed in the new units should have a larger or smaller number. In the previous case, we know that a foot is smaller than a mile, so the distance in feet should have a larger number (792,000) than the distance in miles (150). The conversion factor has the larger number (5280) in the numerator, so it gave a larger number in the answer. 

Most importantly, the conversion factor you choose must cancel all units except those you want in the answer. Therefore, set the unit you are converting from (beginning unit) in the opposite position in the conversion factor (numerator or denominator) so that it cancels and you are left with the unit you are converting to (final unit) ... 

We can choose to make this a two-part problem. We are given the actual yield. The stoichiometry problem for finding MgO must be based on theoretical yield. What is our link between actual and theoretical yield Percent yield gives us the conversion factor 81.3 g (act)/100 g (theo). First we will find the theoretical yield from the actual yield then we will calculate the amount of reactant by stoichiometry. 

Suppose you had guessed wrong and used 1 doUar/4 quarters when choosing which of the two conversion factors to use. You would have an answer with entirely inappropriate units. 

We choose the conversion factor that will introduce the unit meter and cancel the unit centimeter (i.e., the one on the right). We can set up a problem of this type as the following series of unit conversions so that it is unnecessary to calculate an intermediate answer at each step ... 

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