To find the total cost to deliver all the pieces of first-class mail, you multiply the number of pieces of mail by the cost of each stamp.
Given:
- Number of pieces of mail = \( 1.52 \times 10^{10} \)
- Cost of each stamp = $0.55
Now, let's perform the multiplication:
\[ \text{Total Cost} = (1.52 \times 10^{10}) \times 0.55 \]
First, calculate \( 1.52 \times 0.55 \):
\[ 1.52 \times 0.55 = 0.836 \]
Now, since we have the power of ten from the first term, we write:
\[ \text{Total Cost} = 0.836 \times 10^{10} \]
To express this in proper scientific notation, we want the coefficient to be between 1 and 10. Thus:
\[ 0.836 = 8.36 \times 10^{-1} \]
Now we can combine the powers of ten:
\[ 0.836 \times 10^{10} = 8.36 \times 10^{-1} \times 10^{10} = 8.36 \times 10^{9} \]
So, the total cost to deliver all the pieces of mail in scientific notation is:
\[ \boxed{8.36 \times 10^{9}} \]