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

It will depend on how many euros they intend to convert. If they were only converting one euro they would get $1.35 whichever rate they used, but imagine it was a thousand euros .At the correct rate they would get $1352.61, at the proposed rate they would only get $1350.

Answer 2

No, the Ruiz family won't get the correct exchange rate.

Solution-

Suppose the family has 100 euros. Using the actual exchange rate, we find they have

`100* 1.35261=\$135.261`

If we use the rate 1 euro = 1.35 USD(after rounding off), we would have

`100* 1.35 =\$135.00`

It would seem insignificant as it is small, because it is only $0.261. But, the more money they convert with this rate, the more incorrect they will be. If they exchange 1 million euros to dollar with the rounded off rate, they will loose,

`(1,000,000* 1.35261)-(1,000,000* 1.35)=\$2610`

So, they will get $2610 less while exchanging 1 million dollar, if they round off the exchange rate.