Sure, let's walk through this step-by-step.
1. Start with the given value: [tex]\(146 \, \frac{\text{mg}}{\text{dL}}\)[/tex].
2. Convert milligrams to grams:
[tex]\[
146 \, \frac{\text{mg}}{\text{dL}} \times \frac{1 \, \text{g}}{10^3 \, \text{mg}} = 146 \times 10^{-3} \, \frac{\text{g}}{\text{dL}} = 0.146 \, \frac{\text{g}}{\text{dL}}
\][/tex]
3. Convert deciliters to liters:
[tex]\[
0.146 \, \frac{\text{g}}{\text{dL}} \times \frac{1 \, \text{dL}}{10^{-1} \, \text{L}} = 0.146 \times 10 = 1.46 \, \frac{\text{g}}{\text{L}}
\][/tex]
4. Convert liters to milliliters:
[tex]\[
1.46 \, \frac{\text{g}}{\text{L}} \times \frac{10^{-3} \, \text{L}}{1 \, \text{mL}} = 1.46 \times 10^{-3} = 0.00146 \, \frac{\text{g}}{\text{mL}}
\][/tex]
So, the calculations yield the following conversions:
1. [tex]\(0.146 \, \frac{\text{g}}{\text{dL}}\)[/tex],
2. [tex]\(1.46 \, \frac{\text{g}}{\text{L}}\)[/tex], and
3. [tex]\(0.00146 \, \frac{\text{g}}{\text{mL}}\)[/tex].
Hence the full answer is:
[tex]\[
\boxed{0.146 \, \frac{\text{g}}{\text{dL}}, \, 1.46 \, \frac{\text{g}}{\text{L}}, \, 0.00146 \, \frac{\text{g}}{\text{mL}}}
\][/tex]
