What are normal free testosterone levels

This question concerns the relationship between free testosterone levels in all levels of testosterone?
The normal range for total testosterone around 250-1200 ng / dL (nanograms per deciliter). The normal range for free testosterone is approximately 35-155 pg / mL (picograms per milliliter). The amount of testosterone free must be 5% of total testosterone. If the total testosterone level is 407 ng / dl and free testosterone level is 36.9 pg / ml, what is the percentage of total testosterone, free testosterone? I understand that a nanogram is one billionth of a gram and a picogram is one trillionth of a gram, which would mean that there one nanogram picogram 1000. And there are 100 ml in a deciliter. Good luck. Thank you, Joe Conrad
The problem becomes easier to solve when compared with the same units that total testosterone and free testosterone beaches. So let's convert testosterone complete range of pg / ml, whereas it is the path of the same units as testosterone free. 250 ng / dl x 1000 pg / x 1 ng / dl (100 ml) = 2500 pg / ml 1200 ng / dl x 1000 pg / x 1 ng / dl (100 ml) = 12 000 pg / ml is our new range of total testosterone is 2500-12000 pg / ml. If we take 5% of these values, we get 125-600 pg / ml, which curiously does not fall near the range given by the question. If the total testosterone level is of 407 ng / dl, so let's turn this pg / ml was used. 407 ng / dl × 1000 pg / dl ng x1 / (100 ml) = 4070 pg / ml 36.9 pg / ml / 4070 pg / ml x 100 = 0.9% of total testosterone is free testosterone.
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