You have gotten good advice on your particular question, but let me just pipe in with a broader observation. And please don't take this as a criticism. Your question is "basic" and suggests that you are not an expert carb counter. You are not alone, lots of people "get by" without counting carbs, but you can achieve much better control by precisely dosing your mealtime insulin to your actual meal.
My suggestions is that you make it your mission to become an expert carb counter. You have a pump and it gives you very precise control over your insulin, yet without proper carb counts you cannot realize it's potential. I believe that you could become quite a competent carb counting with little effort and drop your A1c below 7%, perhaps dropping your A1c a whole percent. I do hope you would consider trying.
Here is what you could do. You could take a carb counting class at a local diabetes center. You can check out some basic books on carb counting from your local public library (look in the diabetes section). You could purchase "Advanced Carb Counting" by Scheiner (I got it in a three book deal with "Using Insulin" and "Think Like a Pancreas" on amazon). You could take Gary Scheiner's advanced course on carb counting at Type 1 University.
Fiber (in particular, dietary fiber) is by definition, not digestible. When the macronutrients of a food are measured, fiber is put into the carbohydrate bin. So a general rule allows us to subtract out the carbs that can't be digested, namely the fiber.
That is the simple story. I have a long story, but we shall have to leave that for later.
I realise the OP was from the US (and all the answers so far) but can I point out that labelling is a bit different on products in the EU, and I believe this can also apply to products imported to the US from the EU. http://en.wikipedia.org/wiki/Food_energy
This wiki page shows a UK label for rice
of which sugars 0.4
(no difference to in the US)
Further down the label:
This fibre has already been deducted from the carbs.
Doesn't make any real difference in this example but I remember reading about a packet of high fibre crackers from Sweden. but bought in the US.
They had more grams of fibre listed than carbohydrate ,people were subtracting the fibre and then wondering about these magical no carb crackers!
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