To find the total weight of all the babies born in the US in a year, we'll multiply the average weight of a newborn by the number of babies born.
- The average weight of a newborn is \( 7.5 \) pounds.
- The number of babies born each year is \( 4.1 \times 10^6 \).
Now we calculate the total weight:
\[ \text{Total weight} = \text{Average weight} \times \text{Number of babies} \]
\[ \text{Total weight} = 7.5 \times (4.1 \times 10^6) \]
To multiply these numbers, we can first multiply the coefficients:
\[ 7.5 \times 4.1 = 30.75 \]
Now, we include the power of ten:
\[ \text{Total weight} = 30.75 \times 10^6 \]
Next, we convert \( 30.75 \) into scientific notation:
\[ 30.75 = 3.075 \times 10^1 \]
Thus:
\[ 30.75 \times 10^6 = 3.075 \times 10^1 \times 10^6 = 3.075 \times 10^{7} \]
So the approximate total weight in pounds of all the babies born in the US in a year is:
\[ \boxed{3.075 \times 10^7} \]