Chapter 1, Problem 1.109QP

(a)

Interpretation Introduction

Interpretation:  For the given set of blood levels, it should be checked whether it exceeds the CDC’s threshold level or not.

Concept introduction:

• Lead poisoning affects nearly every system in the body and can occur with no symptoms
• The primary source of lead exposure is the deteriorating lead-based paint in older homes
• According to Centers for Disease Control and prevention (CDC), threshold level of lead in the blood is $10\mu g/dL$
• Conversion formula,

  $\begin{array}{l}1g=1\times 10^6\mu g\\ 1mg=1\times 10^3\mu g\\ 1L=10dL\\ 1dL=1\times 10^{2}mL\end{array}$

Explanation of Solution

The threshold level is given in the units of micrograms per deciliter ($10\mu g/dL$) and the given units are grams per litter. So it is needed to convert the given value to the micrograms per deciliter by using the conversion formula,

Here the conversion formula that needed to use is,

$\begin{array}{l}1g=1\times 10^6\mu g\\ 1L=10dL\end{array}$

By using the given conversion formula, the desired unit can be converted as follows,

$\frac{\text{3}\text{.0}\text{×}{\text{10}}^{\text{-4}}\text{g}}{\text{1L}}\text{×}\frac{{\text{1× 10}}^{\text{6}}\text{μg}}{\text{1g}}\text{×}\frac{\text{1}\text{L}}{\text{10}\text{dL}}\text{=}\text{30μg/dL}$

Since, the threshold value of Lead is $\text{10μg}\text{/dL}$, the given value of Lead $\text{30μg/dL}$ in the blood would exceeds the CDC’s threshold level

(b)

Interpretation Introduction

• The threshold level is given in the units of micrograms per deciliter ($10\mu g/dL$) and the given units are milligrams per milli litter. So it is needed to convert the given value to the micrograms per deciliter by using the conversion formula,
• Here the conversion formula that needed to use is,
• $\begin{array}{l}1mg=1\times 10^3\mu g\\ 1dL=1\times 10^{2}mL\end{array}$
• By using the given conversion formula, the desired unit can be converted as follows,
• $\frac{\text{2}\text{.0}{\text{×10}}^{\text{-5}}\text{mg}}{\text{mL}}\text{×}\frac{\text{1}{\text{×10}}^{\text{3}}\text{μg}}{\text{1}\text{mg}}\text{×}\frac{\text{1}{\text{×10}}^{\text{2}}\text{mL}}{\text{1}\text{dL}}\text{=}\text{2}\text{.0μg/dL}$
• Here the given value would not exceed the CDC’s threshold level of $10\mu g/dL$
• Conversion formula,

$\begin{array}{l}1g=1\times 10^6\mu g\\ 1mg=1\times 10^3\mu g\\ 1L=10dL\\ 1dL=1\times 10^{2}mL\end{array}$

Explanation of Solution

The threshold level is given in the units of micrograms per deciliter ($10\mu g/dL$) and the given units are milligrams per milli litter. So it is needed to convert the given value to the micrograms per deciliter by using the conversion formula,

Here the conversion formula that needed to use is,

$\begin{array}{l}1mg=1\times 10^3\mu g\\ 1dL=1\times 10^{2}mL\end{array}$

By using the given conversion formula, the desired unit can be converted as follows,

$\frac{\text{2}\text{.0}{\text{×10}}^{\text{-5}}\text{mg}}{\text{mL}}\text{×}\frac{\text{1}{\text{×10}}^{\text{3}}\text{μg}}{\text{1}\text{mg}}\text{×}\frac{\text{1}{\text{×10}}^{\text{2}}\text{mL}}{\text{1}\text{dL}}\text{=}\text{2}\text{.0μg/dL}$

Here the given value would not exceed the CDC’s threshold level of $10\mu g/dL$

(c)

Interpretation Introduction

Interpretation:  For the given set of blood levels, it should be checked whether it exceeds the CDC’s threshold level or not.

Concept introduction:

• Lead poisoning affects nearly every system in the body and can occur with no symptoms
• The primary source of lead exposure is the deteriorating lead-based paint in older homes
• According to Centers for Disease Control and prevention (CDC), threshold level of lead in the blood is $10\mu g/dL$
• Conversion formula,

  $\begin{array}{l}1g=1\times 10^6\mu g\\ 1mg=1\times 10^3\mu g\\ 1L=10dL\\ 1dL=1\times 10^{2}mL\end{array}$

Explanation of Solution

The threshold level is given in the units of micrograms per deciliter ($10\mu g/dL$) and the given units are grams per centimeter cube. So it is needed to convert the given value to the micrograms per deciliter by using the conversion formula,

Here the conversion formula that needed to use is,

$\begin{array}{l}\text{1}\text{g =}\text{1}{\text{×10}}^{\text{6}}\text{μg}\\ \text{1}{\text{dL=1×10}}^{\text{2}}\text{mL}\end{array}$

By using the given conversion formula, the desired unit can be converted as follows,

$\begin{array}{l}\text{6}\text{.5}{\text{×10}}^{\text{-8}}{\text{g/cm}}^{\text{3}}\text{=}\text{6}\text{.5}{\text{×10}}^{\text{-8}}\text{g/mL}\\ \frac{\text{6}\text{.5}{\text{×10}}^{\text{-8}}\text{g}}{\text{mL}}\text{×}\frac{\text{1}{\text{×10}}^{\text{6}}\text{μg}}{\text{1}\text{g}}\text{×}\frac{\text{1}\text{×}{\text{10}}^{\text{2}}\text{mL}}{\text{1}\text{dL}}\text{=6}\text{.5μg/dL}\end{array}$

$\text{6}\text{.5μg/dL}$ Would not exceed the CDC’s threshold level of $10\mu g/dL$