3 Carmen's water bottle holds \( 1 \frac{8}{10} \) liters of water. Jorge's water bottle holds \( 2 \frac{2}{5} \) liters of water. Part A Jorge says that his bottle holds about \( \frac{1}{2} \) liter more water than Carmen's. Without finding the actual difference, explain why Jorge's estimate is or is not reasonable.

To evaluate Jorge's estimate, let's first convert Carmen's and Jorge's water bottle capacities into improper fractions for easier comparison. Carmen's bottle holds \( 1 \frac{8}{10} \) liters, which is equivalent to \( \frac{18}{10} \) liters or \( 1.8 \) liters. Jorge's bottle holds \( 2 \frac{2}{5} \) liters, which converts to \( \frac{12}{5} \) liters or \( 2.4 \) liters. Now, if we look at the numbers, \( 2.4 \) liters minus \( 1.8 \) liters gives us \( 0.6 \) liters, not \( 0.5 \) liters. Hence, while Jorge's assertion that his bottle holds more water than Carmen's is true, his estimate of about half a liter more is slightly off, making it an unreasonable approximation. This exercise is a great reminder that when estimating differences, even small oversights in addition can lead to inaccuracies in our estimations. It’s always wise to verify our assumptions or take a moment to double-check the math!