To find the total weight of all the babies born in the U.S. in a year, you multiply the average weight of a newborn by the total number of babies born.
- Average weight of a newborn = 7.5 pounds
- Number of babies born per year = \( 4.1 \times 10^6 \)
Now, calculate the total weight:
\[ \text{Total weight} = \text{Average weight} \times \text{Number of babies} \]
\[ \text{Total weight} = 7.5 , \text{pounds} \times 4.1 \times 10^6 \]
First, perform the multiplication of the coefficients:
\[ 7.5 \times 4.1 = 30.75 \]
Then, since we are multiplying by \( 10^6 \), we can express the total weight in scientific notation:
\[ \text{Total weight} = 30.75 \times 10^6 \]
To express this in standard scientific notation (where the coefficient is between 1 and 10), we move the decimal point one place to the left:
\[ 30.75 \times 10^6 = 3.075 \times 10^7 \]
Thus, the approximate total weight of all the babies born in the U.S. in a year is:
\[ \boxed{3.075 \times 10^7} \text{ pounds} \]