To find the total cost of delivering all the pieces of mail, we multiply the number of pieces of mail by the cost of each stamp.
Given:
- Number of pieces of first-class mail = \( 1.52 \times 10^{10} \)
- Cost of each stamp = $0.55
Now we calculate the total cost:
\[ \text{Total Cost} = \text{Number of Pieces} \times \text{Cost per Stamp} \]
\[ \text{Total Cost} = (1.52 \times 10^{10}) \times 0.55 \]
To perform the multiplication, we can multiply the coefficients (1.52 and 0.55) and then adjust for powers of 10:
\[ 1.52 \times 0.55 = 0.836 \]
Now, we include the power of 10:
\[ \text{Total Cost} = 0.836 \times 10^{10} \]
To express this in scientific notation, we need to adjust the coefficient to be between 1 and 10. Thus, we rewrite \( 0.836 \) as \( 8.36 \times 10^{-1} \):
\[ 0.836 \times 10^{10} = 8.36 \times 10^{-1} \times 10^{10} = 8.36 \times 10^{9} \]
Therefore, the total cost in scientific notation is:
\[ \boxed{8.36 \times 10^9} \]