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Think you know the rules about healthy foods and can pick the best-for-you fruit from the produce section? These facts might surprise you.

More than half of Americans say they give a lot of thought to the healthfulness of foods and beverages they consume. But much of what we read and hear about nutrition — from the virtues of fruit juice to the hazards of fat — can steer us to make choices that are less healthful than we think. How many of the following food facts come as a shocker?

1. Imported produce from the supermarket can have higher nutrient levels than local produce from a farmers’ market. The nutritional content of produce is determined by a number of factors, including temperature, light and soil. Though storage and transportation cause some types of produce to lose nutrients, studies show that antioxidants may actually increase in other cases. As counterintuitive as it seems, this means blueberries shipped long distances could be slightly more nutritious than those right off the bush.

2. Foods labeled “no trans fat” may legally contain some. The government allows manufacturers to round down anything less than 0.5 g of trans fat to zero. That means if you eat several servings of a so-called trans-fat-free food — or a few such foods a day — you can wind up consuming measurable amounts of trans fat. To avoid it, check ingredient labels and steer clear of anything containing partially hydrogenated oils. (That may become easier if the Food and Drug Administration’s declaration that trans fats are unsafe holds, and they are banned from foods like doughnuts, baked goods and frozen pizzas.)

3. Decaffeinated coffee is not caffeine-free. Most decaf coffee has some caffeine. A decaf espresso, for example, can have as much as 16 mg. In a decaf latte, which contains two shots of espresso, that adds up to about the same amount of caffeine found in a can of Coke.

4. Canned white tuna has about three times more mercury than chunk light. The species used for white tuna, albacore, is larger and accumulates more mercury than skipjack, which is used for chunk light. The better option? Canned salmon has less mercury than both types of tuna.

5. Fruit juice can have more calories and sugar than soda. An 8-oz. glass of apple juice has roughly 115 calories, compared with about 95 in Coke. A cup of grape juice contains 36 g of sugar — about 9 g more than in the same amount of Pepsi. While the sugar in juice is natural (and not high-fructose corn syrup), it’s still sugar.

6. Not all fiber is created equal. To boost their fiber content, many packaged foods contain added fiber with names such as inulin, maltodextrin and polydextrose. While these count toward a food’s fiber total, they haven’t been proved to offer the same health benefits as the naturally occurring fiber found in fruits, vegetables and whole grains.

7. Cooked vegetables can be more nutritious than raw ones. Whether a vegetable is more nutritious cooked or raw depends on the vegetable, the nutrient and the cooking method. For example, we get more of the antioxidant lycopene from cooked tomatoes than from raw ones. Likewise, boiling carrots increases their levels of antioxidants called carotenoids. But cooking carrots also lowers amounts of other compounds.

8. “Multigrain” products aren’t necessarily whole grain. While multigrain may appear to be a synonym for whole grain or whole wheat — which is associated with a reduced risk of heart disease, diabetes and digestive problems — it’s not. It simply means the food is made from several grains, which may be whole or refined. To make sure the food is rich in whole grains, check the ingredients. The first one listed should contain the word whole.

9. Adding fat to your salad can make it more healthful. Eating vegetables along with fat can help the body better absorb their nutrients. So using a dressing with fat may make a salad with tomatoes and carrots, which are high in fat-soluble carotenoids, more nutritious than using a fat-free one or skipping the dressing altogether.