Problem 24 - Prealgebra

Question

There are a number of online calculators that will show what the money in one country is worth in another country. One such converter, the XE Universal Currency Converter@, uses live, up-to-the-minute currency rates. Use the information shown here to determine what the equivalent to one U.S. dollar for each of the following denominations. Round to the nearest thousandth, where necessary. \(\$ 25.00\) U.S. dollars are equivalent to 2704.0125 Japanese yen

Step-by-Step Solution

Answer

1 USD is equivalent to 108.161 yen.

Step 1: Understand the Problem

We are given the exchange rate involving U.S. dollars (USD) and Japanese yen. We know that $25.00 USD is equivalent to 2704.0125 Japanese yen. We need to find how much 1 U.S. dollar is equivalent to in Japanese yen.

Step 2: Set Up the Conversion Ratio

To find the value of 1 USD in Japanese yen, we need to set up the conversion ratio. If $25.00 USD equals 2704.0125 yen, then 1 USD can be found by dividing the yen amount by the dollar amount, i.e., \[\frac{2704.0125 \text{ yen}}{25 \text{ USD}}.\]

Step 3: Perform the Division

Now, divide the total yen by the number of dollars to find the equivalent for 1 dollar.\[1 \text{ USD} = \frac{2704.0125}{25} = 108.1605 \text{ yen}.\]

Step 4: Round to the Nearest Thousandth

We need to round the result, 108.1605 yen, to the nearest thousandth. The thousandth place is the third digit after the decimal, which is 0 in this case. The digit after it is a 5, so we round up, making it 108.161 yen.

Key Concepts

Exchange Rates

Exchange rates are vital in global finance and travel, allowing for the conversion of one currency to another. When you're dealing with exchange rates, you're essentially finding out how much one currency is worth in terms of another. This is crucial for everything from international trade to personal travel plans. In the exercise given, the exchange rate tells us that $25.00 U.S. dollars are equivalent to 2704.0125 Japanese yen. Knowing the exchange rate is fundamental when planning a budget or assessing costs in a different country's currency. These rates change frequently due to economic factors, so it's essential to use reliable tools, like the XE Currency Converter, for accurate, up-to-minute exchange rates.
Understanding exchange rates helps in making informed financial decisions and ensures we get value for our money when exchanging currencies.

Ratio and Proportion

Ratios and proportions are mathematical tools that help us compare quantities relative to each other. In currency conversion, we often set up a ratio to find equivalent values across different currencies. For instance, the exercise uses a ratio to determine how much 1 U.S. dollar is worth in yen. The initial given ratio is \$25.00 U.S. dollars to 2704.0125 yen.

• To find the exchange rate for 1 USD, divide the yen by the dollars: \[ 1 ext{ USD} = \frac{2704.0125 ext{ yen}}{25 ext{ USD}} \]
• This equation gives us the proportion that 1 U.S. dollar has when converted to yen.

Using ratios simplifies currency conversion and ensures consistency across calculations. By mastering ratios and proportions, you can handle many real-world situations involving comparison of quantities.

Rounding Decimals

Rounding decimals is an essential skill, especially in fields like finance where precision and clarity are paramount. When working with currency, numbers often need to be expressed in a certain format for accuracy and ease of use.
Let's look at how we apply this in our exercise. Once we've calculated the exchange value of 1 U.S. dollar to be 108.1605 yen, we need to round it to the nearest thousandth:

• The thousandth place is the third digit after the decimal point, which in our number is 0 in 108.1605.
• The digit after it (5 in this case) tells us to round up.
• So, 108.1605 rounded to the nearest thousandth becomes 108.161.

Rounding helps simplify numbers without losing significant accuracy in calculations. It's crucial in aligning numbers with specific standards like those used in accounting and financial reporting.