Sometimes reasoning will lead you to an unexpected or surprising result. This does not mean your reasoning is incorrect, but you should be careful in this type of situation.

Example 2

Suppose a 100 g orange is made of 99% water. It is allowed to sit in the sun to dry until it is 98% water. What do you expect the weight of the orange to be now?

Here is the original scenario. There is 1 g of solid for every 99 g of water.

If you adjust the equation to reflect 98% water, you will need to reduce its mass to 49 g, as shown below.

This shows that the orange is 1 g solid and 49 g water, or a total of 50 g, when it is 98% water.

In Example 2, you may have been surprised to find that going from 99% water to 98% water meant the orange's mass was reduced by a half. Although the result is unexpected, you should not dismiss it. Careful reasoning has shown that the conclusion is true.