The <em>correct answer</em> is:
No, the family will not be able to correctly convert their euros to U.S. dollars using the rate 1 euro = 1.35 USD.
Expanation:
Suppose the family has 250 euros. Using the actual exchange rate, we find they have
250(1.35261) = 338.1525 ≈ $338.15
If we use the rate 1 euro = 1.35 USD, we would have
250(1.35) = $337.50.
They would be short $0.65. While this does not seem like a large discrepancy, the more money they convert with this rate, the more incorrect they will be.