Problem 21 - 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. \(\$ 100.00\) U.S. dollars are equivalent to 64.582 euros

Step-by-Step Solution

Answer

1 U.S. dollar is equivalent to 0.646 euros.

Step 1: Understanding the Given Information

We are given that \(\$100.00\) U.S. dollars is equivalent to \(64.582\) euros. We need to find out what \(1\) U.S. dollar is equivalent to in euros.

Step 2: Setting Up the Conversion Equation

To find out the equivalent of \(1\) U.S. dollar, we can set up the equation: \(\$100.00 = 64.582\) euros. We need to divide both sides of the equation by \(100\) to calculate the equivalent in euros for \(1\) U.S. dollar.

Step 3: Performing the Calculation

Divide \(64.582\) euros by \(100\) to get the equivalent of \(1\) U.S. dollar in euros. \[ 1\text{ U.S. dollar} = \frac{64.582}{100} \text{ euros} \] Perform the division to find the result.

Step 4: Rounding the Result

The division gives us \(0.64582\) euros for \(1\) U.S. dollar. Round this result to the nearest thousandth, which results in \(0.646\) euros.

Key Concepts

Mathematical Equations

When you're faced with a currency conversion problem, setting up a mathematical equation is an essential first step. In our example, we know that $100 U.S. dollars is equivalent to 64.582 euros. This information allows us to form an equation: \[ 100\, ext{U.S. dollars} = 64.582\, ext{euros} \] We need to find the value of just one U.S. dollar in euros. To do this, we can adjust our equation to represent this goal. By recognizing that we desire to isolate the value of one U.S. dollar, we revise our initial equation so that it becomes a simpler division task. This transition into division, as the next core concept, steers us toward our final goal of finding the equivalent of one U.S. dollar in euros.

Division

Division is a fundamental mathematical operation used here to simplify and solve our currency conversion problem. Given our modified equation, we need to divide 64.582 euros by 100 to determine how much one U.S. dollar is in euros. This is expressed mathematically as: \[ 1\, ext{U.S. dollar} = \frac{64.582}{100} \, ext{euros} \] By performing this division, we calculate how much a single unit of U.S. currency converts into euros. The division simplifies the proportional relationship between the larger amount (100 dollars) and the smaller unit (1 dollar).Performing the division operation gives a result of 0.64582 euros. This value, however, isn't in its final usable form due to the decimal places extending beyond what is practical for reporting currency values. That's where the concept of rounding comes into play.

Rounding Numbers

After you've calculated a result from a division, such as finding 0.64582 euros for one U.S. dollar, the next step is often rounding. Rounding simplifies the result by reducing the number of decimal places, making it more convenient for everyday applications, especially in contexts like currency conversion where precision to several decimal places isn't necessary. When rounding to the nearest thousandth, you look at the fourth decimal place. If that digit is 5 or greater, you round the third decimal place up by one. In our case, the digit after the third decimal place was 2, so no increase is needed there. When applying rounding rules here: - Third decimal place: 5 - Fourth decimal place: 2 Thus, rounding 0.64582 to the nearest thousandth gives you 0.646. This rounded number is now a more practical and user-friendly representation of the conversion rate for financial or casual calculations.