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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.

Respuesta :

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.
InesWalston

Answer-

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

[tex]100\times 1.35261=\$135.261[/tex]

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

[tex]100\times 1.35 =\$135.00[/tex]

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,

[tex](1,000,000\times 1.35261)-(1,000,000\times 1.35)=\$2610[/tex]

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

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