To find the total weight of all the babies born in the U.S. in a year, we can multiply the average weight of a newborn by the number of babies born.
Given:
- Average weight of a newborn = 7.5 pounds
- Number of babies born = \( 4.1 \times 10^6 \)
Now, we can calculate the total weight:
\[ \text{Total Weight} = \text{Average Weight} \times \text{Number of Babies} \] \[ \text{Total Weight} = 7.5 , \text{pounds} \times 4.1 \times 10^6 \]
Calculating this:
\[ \text{Total Weight} = 30.75 \times 10^6 , \text{pounds} \]
Now we convert this to scientific notation.
\[ 30.75 = 3.075 \times 10^1 \]
So,
\[ 30.75 \times 10^6 = 3.075 \times 10^1 \times 10^6 = 3.075 \times 10^{7} \]
Thus, the approximate total weight of all the babies born in the U.S. in a year is:
\[ \boxed{3.075 \times 10^{7}} , \text{pounds} \]