Persons are medically considered to have lead poisoning if they
have a concentration greater than `10` micrograms of lead per decilitre
of blood. What is the concentration in parts per billion?

Options

A. `1000`
B. `100`
C. `10`
D. `1`

Explanation

To find the concentration of lead in parts per billion (ppb) given that the concentration is greater than 10 micrograms of lead per deciliter of blood, we can follow these steps:

### Step 1: Convert micrograms to grams
The concentration given is 10 micrograms. To convert this to grams, we use the conversion factor:
\[ 1 \text{ microgram} = 10^{-6} \text{ grams} \]
So,
\[ 10 \text{ micrograms} = 10 \times 10^{-6} \text{ grams} = 10^{-5} \text{ grams} \]

### Step 2: Convert deciliters to liters
The volume given is 1 deciliter. We know that:
\[ 1 \text{ deciliter} = 0.1 \text{ liters} \]

### Step 3: Use the formula for concentration in parts per billion (ppb)
The formula to calculate concentration in parts per billion is:
\[ \text{Concentration (ppb)} = \left( \frac{\text{mass of solute (grams)}}{\text{volume of solution (liters)}} \right) \times 10^9 \]

### Step 4: Substitute the values into the formula
Now we can substitute the values we have:
- Mass of solute = \(10^{-5} \text{ grams}\)
- Volume of solution = \(0.1 \text{ liters}\)

Substituting these values into the formula:
\[ \text{Concentration (ppb)} = \left( \frac{10^{-5}}{0.1} \right) \times 10^9 \]

### Step 5: Simplify the expression
Calculating the fraction:
\[ \frac{10^{-5}}{0.1} = 10^{-5} \times 10^{1} = 10^{-4} \]
Now, substituting back into the concentration formula:
\[ \text{Concentration (ppb)} = 10^{-4} \times 10^9 = 10^{5} \text{ ppb} \]

### Final Answer
The concentration of lead in parts per billion is:
\[ 10^{5} \text{ ppb} \]

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