To find the approximate total weight in pounds of all the babies born in the U.S. in a year, we can use the following formula:
\[ \text{Total weight} = \text{Average weight per baby} \times \text{Number of babies} \]
Given:
- The average weight per newborn is \(7.5\) pounds.
- The number of newborns is approximately \(4.1 \times 10^6\).
Now we can calculate the total weight:
\[ \text{Total weight} = 7.5 , \text{pounds} \times 4.1 \times 10^6 , \text{babies} \]
Calculating \(7.5 \times 4.1\):
\[ 7.5 \times 4.1 = 30.75 \]
Now, we multiply \(30.75\) by \(10^6\):
\[ \text{Total weight} \approx 30.75 \times 10^6 \]
To express this in proper scientific notation, we need to adjust \(30.75\):
\[ 30.75 = 3.075 \times 10^1 \]
So, we can rewrite the total weight:
\[ 30.75 \times 10^6 = 3.075 \times 10^1 \times 10^6 = 3.075 \times 10^{1 + 6} = 3.075 \times 10^7 \]
Thus, the approximate total weight in pounds of all the babies born in the U.S. in a year is:
\[ \boxed{3.075 \times 10^7} \text{ pounds} \]