Q29P - Fundamentals Of Physics

Question

 On a spending spree in Malaysia, you buy an ox with a weight of 28.9 piculs in the local unit of weights: 1 picul $\mathbf{=}$100 gins, 1 gin $\mathbf{=}$ 16 tahils, 1 tahil $\mathbf{=}$ 10 chees, and 1 chee $\mathbf{=}$ 10 hoons. The weight of 1 hoon corresponds to a mass of 0.3779 g. When you arrange to ship the ox home to your astonished family, how much mass in kilograms must you declare on the shipping manifest? (Hint: Set up multiple chain-link conversions.)

Step-by-Step Solution

Answer

The mass of ox declare on the shipping manifest is $1.75\times {10}^3 \mathrm{kg}$.

Step 1: Given data

The weight of ox is 28.9 piculs

$$\begin{gathered} 1 \mathrm{picul} = 100 \mathrm{gins} \\ 1\mathrm{gin} = 16 \mathrm{tahil} \\ 1 \mathrm{tahil} =10 \mathrm{chees} \\ 1 \mathrm{chee} =10 \mathrm{hoons} \\ 1 \mathrm{hoon} = 0.3779 \mathrm{g} \end{gathered}$$

Step 2: Understanding the conversion factor

Every measure can be attributed to different units. Such units may be converted between them using a conversion factor. In this problem, multiple chain link conversions are needed to answer the mass of ox in kilograms.

Step 3: Determination of the mass of ox in kilograms

Convert the mass of ox in grams as: 

$$\begin{gathered} \left(28.9 \mathrm{picules}\right) = \left(28.9 \mathrm{picules}\right) \left(\frac{100 \mathrm{gin}}{1 \mathrm{picule}}\right)\left(\frac{16 \mathrm{tahil}}{1 \mathrm{gin}}\right)\left(\frac{10 \mathrm{chee}}{1 \mathrm{tahi}}\right)\left(\frac{10 \mathrm{hoon}}{1 \mathrm{chee}}\right)\left(\frac{.03779 \mathrm{g}}{1 \mathrm{hoon}}\right) \\ =1,747,409.6 \mathrm{g} \end{gathered}$$

Now, convert the mass of ox from g to kg.

$$\begin{gathered} 1,747,409.6 \mathrm{g} = 1,747,409.6 \mathrm{g}.\left(\frac{1 \mathrm{kg}}{{10}^{3 }\mathrm{g}}\right) \\ =1.75\times {10}^3 \mathrm{kg} \end{gathered}$$

Thus, the mass of ox declare on the shipping manifest is$1.75\times {10}^3 \mathrm{kg}$.