To find the total weight in pounds of all the babies born in the U.S. in a year, you can multiply the average weight of a newborn by the number of babies born.
The average weight of a newborn is 7.5 pounds, and the number of babies born each year is approximately \(4.1 \times 10^6\).
Total weight = average weight × number of babies
\[ \text{Total weight} = 7.5 , \text{pounds} \times 4.1 \times 10^6 \]
Now, performing the multiplication:
\[ 7.5 \times 4.1 = 30.75 \]
So, the total weight can be expressed as:
\[ \text{Total weight} = 30.75 \times 10^6 \]
To express \(30.75\) in scientific notation, we move the decimal point one place to the left:
\[ 30.75 = 3.075 \times 10^1 \]
Now we can combine the exponents:
\[ 30.75 \times 10^6 = 3.075 \times 10^1 \times 10^6 = 3.075 \times 10^{7} \]
Thus, the approximate total weight in pounds of all the babies born in the U.S. in a year is:
\[ \boxed{3.075 \times 10^7} \]