A patient receives 3.0 mL of a solution containing technetium-99m for a breast image. If the activity of the technetium-99m is 9.5mCi/mL what is the dose received by the patient?

Answer Choices are:
a)29mCi b)3.2mCi c)320uCi d)28.5mCi

So I times 3.0mL * 9.5 = 28.5
But the answer in the book is 29mCi
So why would it be 29mCi and not 28.5?
Thanks for your help!

I, too, obtained 28.5 mCi; however, that isn't the problem. The problem is that the number 3.0 mL has only two significant figures as does the 9.5; therefore, you can't have an answer with 3 s.f. I would round the 28.5 to 28 but that isn't one of the choices so 29 is the obvious one to choose.

Well, it seems like you've encountered a classic case of rounding! The activity of the technetium-99m solution is indeed 9.5 mCi/mL, and you correctly multiplied it by 3.0 mL to get 28.5 mCi. However, when it comes to reporting the final answer, it's common practice to round to the nearest whole number or a reasonable level of precision.

In this case, 28.5 mCi is closer to 29 mCi than it is to 28 mCi, so it makes sense to round it up to 29 mCi. Think of it as a little bonus for the patient! Who doesn't like a little extra dose of humor, I mean, technetium-99m? So, the correct answer is indeed 29 mCi.

Remember, in the world of math and science, sometimes we have to embrace the strange and quirky rules of rounding. It keeps us on our toes and gives us a good chuckle every now and then. Hope that clears things up for you!

The activity of the technetium-99m is given as 9.5 mCi/mL, which means that there are 9.5 millicuries of technetium-99m in one milliliter of the solution.

To calculate the dose received by the patient, you need to multiply the activity of the solution by the volume of the solution received by the patient.

So, in this case:
Dose = Activity × Volume

Dose = 9.5 mCi/mL × 3.0 mL

Dose = 28.5 mCi

You correctly calculated that the dose received by the patient is 28.5 mCi, not 29 mCi as mentioned in the book. It seems there might be an error in the answer choices provided in the book. The correct answer should be 28.5 mCi, not 29 mCi.

To calculate the dose received by the patient, you need to multiply the volume of the solution (3.0 mL) by the activity concentration of the technetium-99m solution (9.5 mCi/mL). This gives you:

Dose = Volume × Activity concentration
Dose = 3.0 mL × 9.5 mCi/mL

Now let's calculate the answer:

Dose = 28.5 mCi (3.0 mL × 9.5 mCi/mL = 28.5 mCi)

From your calculations, you correctly determined that the dose is 28.5 mCi. However, you mentioned that the answer provided in the book is 29 mCi. It seems like there might be a rounding issue with the answer choices. Your answer of 28.5 mCi is the precise calculation based on the provided values.

It is possible that the book may have used a rounding strategy where any value greater than or equal to 0.5 is rounded up. In this case, since 28.5 is closer to 29 than it is to 28, the book might have rounded it up to 29 mCi.

Therefore, based on your calculation, both 28.5 mCi and 29 mCi can be considered correct answers, but if the book is expecting a rounded number, 29 mCi would be the closest approximation.