Question

If the exchange rate between the Japanese yen and the U.S. dollar expressed in terms of yen per dollar is \(\$ 115=\$ 1\), what is the exchange rate when expressed in terms of dollars per yen?

Short answer

The exchange rate when expressed in terms of dollars per yen is approximately \( \frac{1}{115} \) dollars per yen or approximately 0.0087 dollars per yen.

Step-by-step solution

Understand the Given Exchange Rate

The provided exchange rate is 115 yen for 1 U.S. dollar. This is represented in terms of yen per dollar.

Conversion to dollars per yen

To express the exchange rate in terms of dollars per yen, the reciprocal of the given rate is taken. The reciprocal of a number is found by dividing 1 by the number.

Calculation

Finding the reciprocal of the given rate, which is \( 115 \) yen per dollar, results in approximately \( \frac{1}{115} \) dollars per yen, expressed as a decimal.

Key concepts

Understanding Reciprocal Calculation

Reciprocal calculation is a key skill in mathematics and currency exchange. It's used to find the inverse of a number. When we say 'reciprocal,' we mean flipping the original number. To do this, you divide 1 by the given number.
This is important in exchange rate conversions where you need to switch the terms. For example, to convert from yen per dollar to dollars per yen, we use a reciprocal calculation.

• Step 1: Start with your original number, like 115 yen per dollar.
• Step 2: Find the reciprocal by dividing 1 by 115.
• Step 3: The result, in this case, is approximately 0.0087 dollars per yen.

Understanding this process helps you switch between different ways of expressing exchange rates easily.

Basics of Currency Exchange

Currency exchange is the system of converting one currency into another. It's essential for international trade and tourism. Each country's currency has a value representing how much it can exchange for another currency.

There are two main forms of exchange rates:

• Fixed Rate: The country's government sets this rate against another currency, often the U.S. dollar or the euro.
• Floating Rate: Determined by the market based on supply and demand.

When exchanging currency, understanding the rate and whether it's quoted as unit per foreign currency (e.g., yen per dollar) or foreign currency per unit (e.g., dollars per yen) is vital. Mastering this helps in making informed financial decisions.

Calculating Yen to Dollar Conversion

Converting yen to dollars involves understanding the exchange rate between these two currencies. If the rate is provided in yen per dollar, it tells how many yen you need to get one U.S. dollar.

Converting this rate to dollars per yen involves finding the reciprocal. Here's a quick guide:

• Take the yen per dollar rate, let's say 115 yen per dollar.
• Apply the reciprocal calculation: 1 divided by 115 equals approximately 0.0087 dollars per yen.

This means for every yen, you'd get roughly 0.0087 dollars. Having these conversions at your fingertips allows for quick currency evaluations, crucial for travelers and businesses involved in international dealings.