Others can correct me if I am wrong, but I think the 10th of a teaspoon is likely a minimum amount. Cayenne comes in different strengths, so 1/10th of one type is not equal to 1/10th of another. Like you, I have no idea how much 1/10th of a teaspoon is. I just (liberally) shake the cayenne on top of lime juice and syrup, then add water. I likely use too much cayenne.
Keep up the work. I am on day one also. Feeling a little tired today, but I have been on vacation, and my nutrition habits had strayed a bit.