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 \\(\frac{1.35\text{ usd}}{1\text{ euro unit}}\\). will this give the ruiz family the correct exchange? explain.

Explanation:

Step1: Round actual rate to hundredth

Actual rate: $1.35261$ USD/euro. Round to nearest hundredth: $1.35$ USD/euro (since the thousandths digit 2 < 5, we keep the hundredths digit 5).

Step2: Compare to family's ratio

Family uses $\frac{1.35\ \text{USD}}{1\ \text{euro unit}}$, which matches the rounded official rate. When converting euros to USD, rounding the exchange rate to the nearest hundredth first aligns with how USD are stated (to the nearest hundredth), so the conversion will produce USD values rounded correctly to the required decimal place.

Answer:

Yes, this will give the correct exchange. The actual exchange rate of 1.35261 USD per euro rounds to 1.35 USD per euro (nearest hundredth), which matches the family's conversion ratio. Since USD are stated to the nearest hundredth, using this rounded ratio will result in correctly formatted USD values for the exchange.