\begin{tabular}{|c|c|c|}
\hline Currency & USD/1 Unit & Units/1 USD \\
\hline \begin{tabular}{c}
Canadian \\
dollar
\end{tabular} & 0.97071 & 1.03069 \\
\hline Euro & 1.35261 & 0.73935 \\
\hline \begin{tabular}{c}
Japanese \\
yen
\end{tabular} & 0.01007 & 99.30487 \\
\hline \begin{tabular}{c}
Indian \\
rupee
\end{tabular} & 0.01594 & 62.72053 \\
\hline
\end{tabular}

Which expression can be used to convert 100 USD to Japanese yen?

A. [tex]\(100 \text{ USD} \left(\frac{99.30487 \text{ yen}}{1 \text{ USD}}\right)\)[/tex]

B. [tex]\(100 \text{ USD} \left(\frac{1 \text{ USD}}{99.30487 \text{ yen}}\right)\)[/tex]

C. [tex]\(100 \text{ USD} \left(\frac{0.01007 \text{ yen}}{1 \text{ USD}}\right)\)[/tex]

D. [tex]\(100 \text{ USD} \left(\frac{99.30487 \text{ USD}}{1 \text{ yen}}\right)\)[/tex]



Answer :

To determine the correct expression to convert 100 USD to Japanese yen, we start by analyzing the provided exchange rate table:

[tex]\[ \begin{tabular}{|c|c|c|} \hline Currency & USD/1 Unit & Units/1 USD \\ \hline \begin{tabular}{c} Canadian \\ dollar \end{tabular} & 0.97071 & 1.03069 \\ \hline Euro & 1.35261 & 0.73935 \\ \hline \begin{tabular}{c} Japanese \\ yen \end{tabular} & 0.01007 & 99.30487 \\ \hline \begin{tabular}{c} Indian \\ rupee \end{tabular} & 0.01594 & 62.72053 \\ \hline \end{tabular} \][/tex]

The table provides the exchange rate in two forms for each currency:
1. "USD/1 Unit" - the amount of USD equivalent to 1 unit of the foreign currency.
2. "Units/1 USD" - the amount of foreign currency equivalent to 1 USD.

For converting USD to Japanese yen, we need the "Units/1 USD" rate for Japanese yen, which is given as 99.30487. This means that 1 USD is equivalent to 99.30487 Japanese yen.

To convert 100 USD to Japanese yen, we use the conversion rate of 99.30487 yen per USD:

[tex]\[ 100 \, \text{USD} \times \left(\frac{99.30487 \, \text{Yen}}{1 \, \text{USD}}\right) \][/tex]

The [tex]\( \text{USD} \)[/tex] units cancel out, leaving us with the amount in Japanese yen. Therefore, the expression to convert 100 USD to Japanese yen is:

[tex]\[ 100 \, \text{USD} \times \left(\frac{99.30487 \, \text{Yen}}{1 \, \text{USD}}\right) \][/tex]

So, the correct expression is:

[tex]\[ 100 \, \text{USD} \, \left(\frac{99.30487 \, \text{Yen}}{1 \, \text{USD}}\right) \][/tex]