Q36P - Fundamentals Of Physics

Question

Table 1-7 shows some old measures of liquid volume. To complete the table, what numbers (to three significant figures) should be entered in (a) the wey column, (b) the chaldron column, (c) the bag column, (d) the pottle column, and (e) the gill column, starting from the top down? (f) The volume of 1 bag is equal to 0.1091 m3. If an old story has a witch cooking up some vile liquid in a cauldron of volume 1.5 chaldrons, what is the volume in cubic meters?

     

Step-by-Step Solution

Answer

Step 1: Given data

$\mathbf{1}\mathbf{ }\mathbf{way}\mathbf{=}\frac{\mathbf{10}}{\mathbf{9}}\mathbf{Chaldron}\mathbf{=}\frac{\mathbf{40}}{\mathbf{3}}\mathbf{Bag}\mathbf{=}\mathbf{640}\mathbf{ }\mathbf{Pottle}\mathbf{=}\mathbf{120240}$ 

The volume of 1 bag${}^{\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1091}\mathbf{ }{\mathbf{m}}^{\mathbf{3}}}$ 

Step 2: Understanding the unit conversion

Unit conversion is the conversion between different units of measure for the same quantity, usually through multiplier conversion factors.

Step 3: (a) Determination of values in way column

Use the relationship between wey and chaldron to calculate the first value in first column.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{wey}\mathbf{=}\frac{\mathbf{10}}{\mathbf{9}}\mathbf{Chaldron} \\ \frac{\mathbf{1}\mathbf{\times }\mathbf{9}}{\mathbf{10}}\mathbf{wey}\mathbf{=}\mathbf{1}\mathbf{ }\mathbf{Chaldron} \\ \mathbf{1}\mathbf{ }\mathbf{Chaldron}\mathbf{=}\frac{\mathbf{9}}{\mathbf{10}}\mathbf{ }\mathbf{wey}\mathbf{ } \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{900}\mathbf{ }\mathbf{way}\mathbf{ } \end{gathered}$$

Use the relationship between wey and bag to calculate the next value.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{wey}\mathbf{=}\frac{40}{3}\mathit{b}\mathit{a}\mathit{g} \\ \frac{\mathbf{1}\mathbf{\times }\mathbf{3}}{\mathbf{40}}\mathbf{wey}\mathbf{=}\mathbf{1}\mathbf{ }\mathit{b}\mathit{a}\mathit{g} \\ \mathbf{1}\mathbf{ }\mathit{b}\mathit{a}\mathit{g}\mathbf{=}\mathbf{7}\mathbf{.}\mathbf{50}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathbf{ }\mathbf{ }\mathbf{wey} \end{gathered}$$

Thus, ${}^{\mathbf{1}\mathbf{ }\mathbf{bag}}$ is equal to ${}^{\mathbf{7}\mathbf{.}\mathbf{50}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathbf{ }\mathbf{ }\mathbf{wey}}$

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{=}\mathbf{640}\mathbf{ }\mathbf{pottle} \\ \mathbf{1}\mathbf{ }\mathbf{pottle}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{56}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}\mathbf{ }}\mathbf{way}\mathbf{ } \end{gathered}$$

Therefore, ${}^{\mathbf{1}\mathbf{ }\mathbf{pottle}}$ is equal to ${}^{\mathbf{1}\mathbf{.}\mathbf{56}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}\mathbf{ }}\mathbf{way}\mathbf{ }}$ .

Use the relationship between wey and pottle to calculate the next value.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{=}\mathbf{120240}\mathbf{ }\mathbf{gill} \\ \mathbf{1}\mathbf{ }\mathbf{gill}\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{32}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}\mathbf{ }}\mathbf{way}\mathbf{ } \end{gathered}$$

Therefore, ${}^{\mathbf{1}\mathbf{ }\mathbf{gill}}$ is equal to${}^{\mathbf{8}\mathbf{.}\mathbf{32}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}\mathbf{ }}\mathbf{way}\mathbf{ }}$.

Step 4: (b) Determination of values in chaldron column

As the conversion is from chaldron to chaldron, it will be 1.00.

Use the relationship between bag and chaldron to calculate the next value.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{=}\frac{\mathbf{10}}{\mathbf{9}}\mathbf{ }\mathbf{chaldron} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\frac{\mathbf{40}}{\mathbf{3}}\mathbf{Bag} \end{gathered}$$

Therefore, 

$$\begin{gathered} \frac{\mathbf{10}}{\mathbf{9}}\mathbf{ }\mathbf{chaldron}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{40}}{\mathbf{3}}\mathbf{Bag} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{1}\mathbf{ }\mathbf{bag}\mathbf{=}\frac{\mathbf{10}\mathbf{\times }\mathbf{3}}{\mathbf{9}\mathbf{\times }\mathbf{40}}\mathbf{Chaldron} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{8}\mathbf{.}\mathbf{33}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathbf{ }\mathbf{Chaldron} \end{gathered}$$

Therefore, ${}^{\mathbf{1}\mathbf{ }\mathbf{bag}}$ is equal to ${}^{\mathbf{8}\mathbf{.}\mathbf{33}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathbf{ }\mathbf{Chaldron}}$.

Use the relationship between pottle and chaldron to calculate the next value.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{=}\frac{\mathbf{10}}{\mathbf{9}}\mathbf{ }\mathbf{chaldron} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{640}\mathbf{ }\mathbf{pottle} \end{gathered}$$

Therefore, 

$$\begin{gathered} \frac{\mathbf{10}}{\mathbf{9}}\mathbf{ }\mathbf{chaldron}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{640}\mathbf{ }\mathbf{pottle} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{1}\mathbf{ }\mathbf{pottle}\mathbf{=}\frac{\mathbf{10}}{\mathbf{9}\mathbf{\times }\mathbf{640}}\mathbf{ }\mathbf{chaldron}\mathbf{ } \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{1}\mathbf{.}\mathbf{74}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{ }\mathbf{chaldron} \end{gathered}$$

Use the relationship between gill and chaldron to calculate the next value.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{=}\frac{\mathbf{10}}{\mathbf{9}}\mathbf{ }\mathbf{chaldron} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{120240}\mathbf{ }\mathbf{gill} \end{gathered}$$

Therefore 

$$\begin{gathered} \frac{\mathbf{10}}{\mathbf{9}}\mathbf{ }\mathbf{chaldron}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{120240}\mathbf{ }\mathbf{gill} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{1}\mathbf{ }\mathbf{gill}\mathbf{=}\frac{\mathbf{10}}{\mathbf{9}\mathbf{\times }\mathbf{120240}}\mathbf{ }\mathbf{chaldron} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{9}\mathbf{.}\mathbf{24}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{ }\mathbf{chaldron} \end{gathered}$$

Thus, ${}^{\mathbf{1}\mathbf{ }\mathbf{gill}}$ is equal to ${}^{\mathbf{9}\mathbf{.}\mathbf{24}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{ }\mathbf{chaldron}}$ .

Step 5: (c) Determination of values in bag column

Use the relationship between chaldron and bag to calculate the next value.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{=}\frac{\mathbf{40}}{\mathbf{3}}\mathbf{Bag} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{10}}{\mathbf{9}}\mathbf{ }\mathbf{chaldron} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ } \end{gathered}$$

Therefore, 

$$\begin{gathered} \frac{\mathbf{40}}{\mathbf{3}}\mathbf{Bag}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{10}}{\mathbf{9}}\mathbf{ }\mathbf{chaldron} \\ \mathbf{1}\mathbf{ }\mathbf{chaldron}\mathbf{=}\frac{\mathbf{40}\mathbf{\times }\mathbf{9}}{\mathbf{3}\mathbf{\times }\mathbf{10}}\mathbf{ }\mathbf{bag} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{12}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{bag} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ } \end{gathered}$$

Therefore, ${}^{\mathbf{1}\mathbf{ }\mathbf{chaldron}}$ is equal to ${}^{\mathbf{12}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{bag}}$ .

As the conversion is from bag to bag, the next value will be 1.00

To calculate the next value, use the relationship between pottle and bag.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{=}\frac{\mathbf{40}}{\mathbf{3}}\mathbf{ }\mathbf{bag} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{640}\mathbf{ }\mathbf{pottle} \end{gathered}$$

Therefore,

$$\begin{gathered} \frac{\mathbf{40}}{\mathbf{3}}\mathbf{ }\mathbf{bag}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{640}\mathbf{ }\mathbf{pottle} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{1}\mathbf{ }\mathbf{pottle}\mathbf{=}\frac{\mathbf{40}}{\mathbf{3}\mathbf{\times }\mathbf{640}}\mathbf{ }\mathbf{bag} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{2}\mathbf{.}\mathbf{08}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathbf{ }\mathbf{bag} \end{gathered}$$

Therefore, ${}^{\mathbf{1}\mathbf{ }\mathbf{pottle}}$ is equal to ${}^{\mathbf{2}\mathbf{.}\mathbf{08}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathbf{ }\mathbf{bag}}$.

Use the relationship between gill and bag, to calculate the next value.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{=}\frac{\mathbf{40}}{\mathbf{3}}\mathbf{ }\mathbf{bag} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{120240}\mathbf{ }\mathbf{gill} \end{gathered}$$

Therefore,

$$\begin{gathered} \frac{\mathbf{40}}{\mathbf{3}}\mathbf{ }\mathbf{bag}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{120240}\mathbf{ }\mathbf{gill} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{1}\mathbf{ }\mathbf{gill}\mathbf{=}\frac{\mathbf{40}}{\mathbf{3}\mathbf{\times }\mathbf{120240}}\mathbf{bag} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{11}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}\mathbf{ }\mathbf{bag} \end{gathered}$$

Step 6: (d) Determination of values in pottle column

To calculate the next value, use the relation between chaldron and pottle.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{ }\mathbf{=}\mathbf{640}\mathbf{ }\mathbf{pottle} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\frac{\mathbf{10}}{\mathbf{9}}\mathbf{chaldron} \end{gathered}$$

Then,

$$\begin{gathered} \mathbf{640}\mathbf{ }\mathbf{pottle}\mathbf{=}\frac{\mathbf{10}}{\mathbf{9}}\mathbf{chaldron} \\ \mathbf{1}\mathbf{ }\mathbf{chaldron}\mathbf{=}\frac{\mathbf{640}\mathbf{\times }\mathbf{9}}{\mathbf{10}}\mathbf{ }\mathbf{pottle} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{576}\mathbf{ }\mathbf{pottle} \end{gathered}$$

Therefore, ${}^{\mathbf{1}\mathbf{ }\mathbf{chaldron}}$ is equal to ${}^{\mathbf{576}\mathbf{ }\mathbf{pottle}}$.

Use the relation between bag and pottle to calculate the next value.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{ }\mathbf{=}\mathbf{640}\mathbf{ }\mathbf{pottle} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\frac{\mathbf{40}}{\mathbf{3}}\mathbf{bag} \end{gathered}$$

Then,

$$\begin{gathered} \mathbf{640}\mathbf{ }\mathbf{pottle}\mathbf{=}\frac{\mathbf{40}}{\mathbf{3}}\mathbf{bag} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{1}\mathbf{ }\mathbf{bag}\mathbf{=}\frac{\mathbf{640}\mathbf{\times }\mathbf{3}}{\mathbf{40}}\mathbf{pottle} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{48}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{pottle} \end{gathered}$$

${}^{\mathbf{48}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{pottle}}$.Thus, ${}^{\mathbf{1}\mathbf{ }\mathbf{bag}}$ is equal to

As the conversion is from pottle to pottle, it will be 1.00.

To calculate the next value, use the relation between gill and pottle. 

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{ }\mathbf{=}\mathbf{640}\mathbf{ }\mathbf{pottle} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{120240}\mathbf{ }\mathbf{gill} \end{gathered}$$

Then, 

$$\begin{gathered} \mathbf{640}\mathbf{ }\mathbf{pottle}\mathbf{=}\mathbf{120240}\mathbf{ }\mathbf{gill} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{1}\mathbf{ }\mathbf{gill}\mathbf{=}\frac{\mathbf{640}}{\mathbf{120240}}\mathbf{ }\mathbf{pottle} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{32}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{ }\mathbf{ }\mathbf{pottle} \end{gathered}$$

Therefore, ${}^{\mathbf{1}\mathbf{ }\mathbf{gill}}$ is equal to ${}^{\mathbf{5}\mathbf{.}\mathbf{32}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{ }\mathbf{ }\mathbf{pottle}}$ .

Step 7: (e) Determination of values in gill column

Use the relation between chaldron and gill to find the next value.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{ }\mathbf{=}\mathbf{120240}\mathbf{ }\mathbf{gill} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\frac{\mathbf{10}}{\mathbf{9}}\mathbf{ }\mathbf{childron} \end{gathered}$$

Then,

$$\begin{gathered} \mathbf{120240}\mathbf{ }\mathbf{gill}\mathbf{ }\mathbf{=}\frac{\mathbf{10}}{\mathbf{9}}\mathbf{ }\mathbf{childron} \\ \mathbf{1}\mathbf{ }\mathbf{chaldron}\mathbf{=}\frac{\mathbf{120240}\mathbf{\times }\mathbf{9}}{\mathbf{10}}\mathbf{ }\mathbf{gill} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{08}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}\mathbf{ }\mathbf{gill}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ } \end{gathered}$$

Therefore, ${}^{\mathbf{1}\mathbf{ }\mathbf{childron}}$ is equal to ${}^{\mathbf{1}\mathbf{.}\mathbf{08}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}\mathbf{ }\mathbf{gill}}$

Use the relationship between bag and gill to find the next value.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{ }\mathbf{=}\mathbf{120240}\mathbf{ }\mathbf{gill} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\frac{\mathbf{40}}{\mathbf{3}}\mathbf{ }\mathbf{bag} \end{gathered}$$

Then,

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathit{b}\mathit{a}\mathit{g}\mathbf{=}\frac{\mathbf{120240}\mathbf{\times }\mathbf{3}}{40}\mathbf{ }\mathbf{gill} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{9}\mathbf{.}\mathbf{02}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{ }\mathbf{gill} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ } \end{gathered}$$

Therefore, ${}^{\mathbf{1}\mathbf{ }\mathbf{bag}}$ is equal to ${}^{\mathbf{9}\mathbf{.}\mathbf{02}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{ }\mathbf{gill}}$ .

Use the relation between pottle and gill to calculate the next value.

$$\begin{gathered} \mathbf{1}\mathbf{ }\mathbf{way}\mathbf{ }\mathbf{=}\mathbf{120240}\mathbf{ }\mathbf{gill} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{640}\mathbf{ }\mathbf{pottle} \end{gathered}$$

Then,

$$\begin{gathered} \mathbf{120240}\mathbf{ }\mathbf{gill}\mathbf{=}\mathbf{640}\mathbf{ }\mathbf{pottle} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{1}\mathbf{pottle}\mathbf{ }\mathbf{=}\frac{\mathbf{120240}}{\mathbf{640}}\mathbf{ }\mathbf{gill} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{187}\mathbf{.}\mathbf{87}\mathbf{ }\mathbf{gill} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{188}\mathbf{ }\mathbf{gill} \end{gathered}$$

Therefore, ${}^{\mathbf{1}\mathbf{ }\mathbf{pottle}}$is equal to ${}^{\mathbf{188}\mathbf{ }\mathbf{gill}}$.

As the conversion is from gill to gill, it will be 1.00.

Step 8: (f) Determination of the volume in cubic meter

It is given that,

$\mathbf{1}\mathbf{ }\mathbf{bag}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{1091}\mathbf{ }{\mathbf{m}}^{\mathbf{3}}$

from part (c), ${}^{\mathbf{1}\mathbf{ }\mathbf{chaldron}\mathbf{=}\mathbf{12}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{bag}}$

Therefore,

$$\begin{gathered} \mathbf{1}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{chaldron}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{\times }\mathbf{12}\mathbf{.}\mathbf{0}\mathbf{ }\mathbf{bag} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{18}\mathbf{ }\mathbf{bag} \end{gathered}$$

Each bag is ${}^{\mathbf{0}\mathbf{.}\mathbf{1091}\mathbf{ }{\mathbf{m}}^{\mathbf{3}}}$

$$\begin{gathered} \mathbf{1}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{childron}\mathbf{=}\mathbf{18}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{1091}\mathbf{ }{\mathbf{m}}^{\mathbf{3}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{196}\mathbf{ }{\mathbf{m}}^{\mathbf{3}} \end{gathered}$$

Therefore, the volume of ${}^{\mathbf{1}\mathbf{.}\mathbf{5}\mathbf{ }\mathbf{chaldron}}$ is ${}^{\mathbf{1}\mathbf{.}\mathbf{96}\mathbf{ }{\mathbf{m}}^{\mathbf{3}}}$ .