To find the total weight of all the babies born in the U.S. in a year, we can use the formula:
\[ \text{Total Weight} = \text{Average Weight per Baby} \times \text{Number of Babies Born} \]
Given:
- Average weight of a newborn = 7.5 pounds
- Number of babies born = \( 4.1 \times 10^6 \) babies
Now, we can calculate the total weight:
\[ \text{Total Weight} = 7.5 , \text{pounds} \times 4.1 \times 10^6 , \text{babies} \]
Calculating this:
\[ 7.5 \times 4.1 = 30.75 \]
Now we incorporate the scientific notation:
\[ \text{Total Weight} = 30.75 \times 10^6 , \text{pounds} \]
To convert \(30.75\) into scientific notation, we rewrite it as \(3.075 \times 10^1\):
Now we adjust the expression:
\[ 30.75 \times 10^6 = 3.075 \times 10^1 \times 10^6 = 3.075 \times 10^{7} \]
So, the total weight of all the babies born in the U.S. in a year is approximately:
\[ \boxed{3.075 \times 10^7} \text{ pounds} \]