Question

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.

Answer 1

No, by rounding the conversion ratio, the Ruiz family will not be getting the most accurate answer. Using the more accurate conversion ratio will give an answer with more than 2 decimal places so the answer can accurately be rounded after the conversion.

Answer 2

So, the question is, whether using the ratio of 1.35261 will give the same results as using the ration of 1.35 if the final answer has to be rounded to the hundreth places anyway.

let's try for 10 euros:

10*1.35=13.5 dollars
10*1.35261=13.5261, rounded to 100th: 13.5 the same!!!


Let's try for 250 dollars:


250*1.35=337.5 dollars
250*1.35261=338.1525, rounded to 100th: 338.12

so, if they use the exact exchange rate, they get more dollars!

In fact the more they exchange, the bigger the difference will be ,as for each dollar exchanged the difference is 0.00261.

So they better use the exact exchange rate!