Question: The diameter of a hydrogen atom is about $1.05 \times 10^{-10}$ meters. A protein molecule has an overall length of 3000 times (or $3 \times 10^{3}$ times) the diameter of a hydrogen atom.
What is the length of the protein molecule, in meters, if it were written in scientific notation?
1. **State the problem:** We need to find the length of a protein molecule given that it is $3 \times 10^{3}$ times the diameter of a hydrogen atom, which is $1.05 \times 10^{-10}$ meters.
2. **Formula:** Length of protein molecule = (Number of times) $\times$ (Diameter of hydrogen atom)
3. **Substitute the values:**
$$\text{Length} = (3 \times 10^{3}) \times (1.05 \times 10^{-10})$$
4. **Multiply the coefficients and add the exponents:**
$$3 \times 1.05 = 3.15$$
$$10^{3} \times 10^{-10} = 10^{3 + (-10)} = 10^{-7}$$
5. **Combine the results:**
$$\text{Length} = 3.15 \times 10^{-7}$$ meters
6. **Final answer:** The length of the protein molecule in scientific notation is
$$\boxed{3.15 \times 10^{-7}}$$ meters.