The Ruiz family is exchanging euros for US dollars. The exchange rate is 1 euro equals 1.35261 USD. Since the Ruiz family knows that USD are stated to the nearest hundredth of a dollar, they used the conversion ratio. Will this give the Ruiz family the correct exchange? Explain.
The correct answer and explanation is:
The Ruiz family wants to convert euros to US dollars using the exchange rate of 1 euro = 1.35261 USD. Since US dollars are typically rounded to the nearest cent (hundredth of a dollar), they plan to use this conversion ratio directly.
Using the conversion ratio of 1.35261 USD per euro is correct because it represents the precise exchange rate. When converting, the family multiplies the amount in euros by this rate to get the amount in USD. However, because US dollars are only expressed to two decimal places, the final dollar amount must be rounded to the nearest cent.
For example, if they have 10 euros:
- Multiply 10 euros by 1.35261 USD/euro = 13.5261 USD
- Round 13.5261 USD to the nearest cent = 13.53 USD
The key point is that the exchange rate should be applied with its full precision first. Only after converting the total amount should rounding to the nearest cent occur. If the family rounds the exchange rate itself before converting, such as rounding 1.35261 to 1.35 or 1.36, this would introduce an error in the conversion that accumulates depending on the amount exchanged.
Therefore, using the full exchange rate value and then rounding the final dollar amount ensures the most accurate and fair conversion. This is important because even small rounding differences in the rate can result in noticeable discrepancies when converting large sums.
In summary, the correct method is to use the exact exchange rate (1.35261) to calculate the USD equivalent first, then round the final converted amount to two decimal places since USD transactions do not use fractions of a cent. This approach guarantees the Ruiz family receives the correct exchange amount consistent with common financial standards.