Q6P - Fundamentals Of Physics

Question

You can easily convert common units and measures electronically, but you still should be able to use a conversion table, such as those in Appendix D. Table 1-6 is part of a conversion table for a system of volume measures once common in Spain; a volume of 1 fanega is equivalent to 55.501 dm3 (cubic decimeters). To complete the table, what numbers (to three significant figures) should be entered in (a) the cahiz column, (b) the fanega column, (c) the cuartilla column, and (d) the almude column, starting with the top blank? Express 7.00 almudes in (e) medios, (f) cahizes, and (g) cubic centimeters (cm3)

                                         

Step-by-Step Solution

Answer

$$\begin{gathered} \left(\mathrm{a}\right)\mathrm{The} \mathrm{numbers} \mathrm{that} \mathrm{should} \mathrm{be} \mathrm{entered} \mathrm{in} \mathrm{Cahiz} \mathrm{column} \mathrm{are}: \\ 1 \mathrm{fanega}=8.33\times {10}^{-2} \mathrm{cahiz} , 1 \mathrm{curtilla}=2.08\times {10}^{-2} \mathrm{cahiz}, \\ 1 \mathrm{almude}=6.94\times {10}^{-3} \mathrm{cahiz} , 1 \mathrm{medio}=3.47\times {10}^{-3} \mathrm{cahiz} \\ \left(\mathrm{b}\right)\mathrm{The} \mathrm{numbers} \mathrm{that} \mathrm{should} \mathrm{be} \mathrm{entered} \mathrm{in} \mathrm{Fanega} \mathrm{column} \mathrm{are}: \\ 1 \mathrm{cutilla}=0.25 \mathrm{fanega}, 1 \mathrm{almude}=8.33\times {10}^{-2} \mathrm{fanega} , \\ 1 \mathrm{medio}=4.17\times {10}^{-2} \mathrm{fanega} \\ \left(\mathrm{c}\right)\mathrm{The} \mathrm{numbers} \mathrm{that} \mathrm{should} \mathrm{be} \mathrm{entered} \mathrm{in} \mathrm{Curtilla} \mathrm{column} \mathrm{are}: \\ 1 \mathrm{almude}=0.333 \mathrm{curtilla} \mathrm{and} 1 \mathrm{medio}=0.167 \mathrm{curtilla} \\ \left(\mathrm{d}\right)\mathrm{The} \mathrm{numbers} \mathrm{that} \mathrm{should} \mathrm{be} \mathrm{entered} \mathrm{in} \mathrm{Almude} \mathrm{column} \mathrm{are}: \\ 1 \mathrm{medio}=0.5 \mathrm{almude} \\ \left(\mathrm{e}\right)7 \mathrm{almude}=14 \mathrm{medio} \\ \left(\mathrm{f}\right)7 \mathrm{almude}=4.86\times {10}^{-2} \mathrm{cahiz} \\ \left(\mathrm{g}\right)7 \mathrm{almude}=3.24\times {10}^{-4} {\mathrm{cm}}^3 \end{gathered}$$

Step 1: Given data

The conversion factors given in the problem are listed below:

The conversion factor from fanega to cahiz is$12 \mathrm{fanega} = 1 \mathrm{cahiz}$ 

The conversion factor from fanega to cahiz is $1 \mathrm{cahiz} = 48 \mathrm{curtilla}$.

The conversion factor from cahiz to cutilla is $1 \mathrm{cahiz} = 144 \mathrm{almude}$

The conversion factor from cahiz  to almude is $1 \mathrm{cahiz} = 288 \mathrm{medio}$

The conversion factor from  cahiz to medio is $1 \mathrm{fanega} = 4\mathrm{curtilla}$

The conversion factor from fanega to curtilla is $1 \mathrm{fanega} = 12 \mathrm{almude}$

The conversion factor from fanega to almude is, $1 \mathrm{fanega} = 24 \mathrm{medio}$

The conversion factor from fanega to medio is, $1 \mathrm{curtilla} = 3 \mathrm{almude}$

The conversion factor from curtilla to almude is, $1 \mathrm{curtilla} =6 \mathrm{medio}$

The conversion factor from curtilla to medio is, $1 \mathrm{almude} = 2 \mathrm{medio}$

The conversion factor from almude to medio is, $1 \mathrm{almude} = 2 \mathrm{medio}$.

Step 2: Understanding the conversion factors

Unit conversion is the conversion between different units of measure for the same quantity, usually through multiplier conversion factors. Use the given conversion factors to convert the quantities from one unit to other.

Step 3: (a) Conversion of the given units to Cahiz

Cahiz column:

$$\begin{gathered} 1)\mathrm{The} \mathrm{given} \mathrm{conversion} \mathrm{factor} \mathrm{is} 12 \mathrm{fanega}=1 \mathrm{cahiz}. \\ 1 \mathrm{fanega}=\frac{1}{12}\mathrm{cahiz} \\ =8.33\times {10}^{-2} \mathrm{cahiz} \\ \mathrm{Therefore}, 1 \mathrm{fanega} \mathrm{is} \mathrm{is} 8.33\times {10}^{-2} \mathrm{cahiz} \\ 2)\mathrm{The} \mathrm{given} \mathrm{conversion} \mathrm{factor} \mathrm{is} 1 \mathrm{cahiz}= 48 \mathrm{curtilla} \\ 1 \mathrm{curtilla}=\left(\frac{1}{48}\right) \mathrm{cahiz} \\ =2.08\times {10}^{-2} \mathrm{cahiz} \\ \mathrm{Therefore},1 \mathrm{curtilla} \mathrm{is} 2.08\times {10}^{-2} \mathrm{cahiz} \\ 3)\mathrm{The} \mathrm{given} \mathrm{conversion} \mathrm{factor} \mathrm{is} 1\mathrm{cahiz} =144 \mathrm{almude} \\ \mathrm{Thus}, \\ 1 \mathrm{almude}=\frac{1}{144}\mathrm{cahiz} \\ =6.94\times {10}^{-3} \mathrm{cahiz} \\ \mathrm{Therefore}, \mathrm{is} \\ 4)\mathrm{The} \mathrm{given} \mathrm{conversion} \mathrm{factor} \mathrm{is} 1 \mathrm{cahiz} =288 \mathrm{medio} \\ 1 \mathrm{medio}=\left(\frac{1}{288}\right) \mathrm{cahiz} \\ =3.47\times {10}^{-3} \mathrm{cahiz} \\ \mathrm{Therefore}, 1 \mathrm{medio} \mathrm{is} 3.47\times {10}^{-3} \mathrm{cahiz} . \end{gathered}$$

Step 4: (b) Conversion of the given units to Fanega

Fanega column:

 $$\begin{gathered} 1)\mathrm{The} \mathrm{given} \mathrm{conversion} \mathrm{factor} \mathrm{is} 1 \mathrm{fanega}=4 \mathrm{curtilla} \\ 1 \mathrm{curtilla}=\left(\frac{1}{4}\right) \mathrm{fanega} \\ =0.25 \mathrm{fanega} \\ \mathrm{Therefore}, 1\mathrm{curtilla} \mathrm{is} 0.25 \mathrm{fanega} \\ 2)\mathrm{The} \mathrm{given} \mathrm{conversion} \mathrm{factor} \mathrm{is}, 1 \mathrm{fanega} \\ \mathrm{So}, \\ \mathrm{Therefore},1 \mathrm{almude} \mathrm{is} 8.33\times {10}^{-2} \mathrm{fanega} \\ 3)\mathrm{The} \mathrm{given} \mathrm{conversion} \mathrm{factor} \mathrm{is}, 1 \mathrm{fanega} =24 \mathrm{medio} \\ 1 \mathrm{medio}=\left(\frac{1}{24}\right) \mathrm{fanega} \\ =4.17\times {10}^{-2} \mathrm{fanega} \\ \mathrm{So}, 1 \mathrm{medio} \mathrm{is} 4.17\times {10}^{-2} \mathrm{fanega} \end{gathered}$$

Step 5: (c) Conversion of the given units to Curtilla

Curtilla column:

$$\begin{gathered} 1)\mathrm{The} \mathrm{given} \mathrm{conversion} \mathrm{factor} \mathrm{is} 1 \mathrm{cutilla}=3 \mathrm{almude} \\ 1 \mathrm{almude}=\frac{1}{3}\mathrm{curtilla} \\ \mathrm{So}, 1 \mathrm{almude} \mathrm{is} 0.333 \mathrm{curtilla}. \\ 2)\mathrm{The} \mathrm{given} \mathrm{conversion} \mathrm{factor} \mathrm{is} 1 \mathrm{curtilla}=6 \mathrm{medio} \\ 1 \mathrm{medio}=\left(\frac{1}{6}\right) \mathrm{curtilla} \\ =0.167 \mathrm{curtilla} \\ \mathrm{So},1 \mathrm{medio} \mathrm{is} 0.167 \mathrm{curtilla} . \end{gathered}$$

Step 6: (d) Conversion of the given units to Almude

Almude column:

$$\begin{gathered} \mathrm{The} \mathrm{given} \mathrm{conversion} \mathrm{factor} \mathrm{is} 1 \mathrm{almude}=2 \mathrm{medio}. \\ 1 \mathrm{medio}=\left(\frac{1}{2}\right)\mathrm{almude} \\ =0.5 \mathrm{almude} \\ \mathrm{So}, 1 \mathrm{medio} \mathrm{is} 0.5 \mathrm{almude} . \end{gathered}$$

Step 7: (e) Conversion of the given units to medio

$$\begin{gathered} \mathrm{The} \mathrm{given} \mathrm{conversion} \mathrm{factor} \mathrm{is} 1 \mathrm{almude}=2 \mathrm{medio}. \\ 7 \mathrm{almude}=7\times 2 \mathrm{medio} \\ =14 \mathrm{medio} \\ \mathrm{Therefore}, 7 \mathrm{almude} \mathrm{is} 14 \mathrm{medio} . \end{gathered}$$

Step 8: (f) Conversion of the given units to cahiz

$$\begin{gathered} 1 \mathrm{almude}=\frac{1}{144}\mathrm{cahiz} \\ =6.94\times {10}^{-3 }\mathrm{cahiz} \\ \mathrm{So}, \\ 7 \mathrm{almude}= 7\times 6.94\times {10}^{-3 }\mathrm{cahiz} \\ =4.86\times {10}^{-2 }\mathrm{cahiz} \\ \mathrm{Therefore}, 7 \mathrm{almude} \mathrm{is} 4.86\times {10}^{-2 }\mathrm{cahiz} \end{gathered}$$

Step 9: (g) Conversion of the given units to centimeters

$$\begin{gathered} 1 \mathrm{almude}=\frac{1}{12}\mathrm{fanega} \\ =8.33\times {10}^{-2^{ }}\mathrm{fanega} \\ 1 \mathrm{fanega}=55.501 {\mathrm{dm}}^3 \\ =55501 {\mathrm{cm}}^3 \\ 7 \mathrm{almude}=7\times 8.33\times {10}^{-2}\times \left(55501\right) {\mathrm{cm}}^3 \\ =3.24\times {10}^{-4} {\mathrm{cm}}^3 \\ \mathrm{Therefore}, 7 \mathrm{almude} \mathrm{is} 3.24\times {10}^{-4} {\mathrm{cm}}^3. \end{gathered}$$