To find out how many years it will take for the bank deposit to yield \(6.42 \times 10^4\) dollars in interest, we can use the formula:
\[ \text{Number of years} = \frac{\text{Total Interest}}{\text{Interest per year}} \]
Given that the total interest desired is \(6.42 \times 10^4\) dollars and the interest per year is \(802.50\) dollars, we can substitute these values into the formula:
\[ \text{Number of years} = \frac{6.42 \times 10^4}{802.50} \]
First, calculate \(802.50\) in scientific notation:
\[ 802.50 = 8.025 \times 10^2 \]
Now we can express the number of years as:
\[ \text{Number of years} = \frac{6.42 \times 10^4}{8.025 \times 10^2} \]
This simplifies to:
\[ \text{Number of years} = \frac{6.42}{8.025} \times \frac{10^4}{10^2} \]
This can be further simplified to:
\[ \text{Number of years} = \frac{6.42}{8.025} \times 10^{4-2} \]
Calculating the numerical value:
\[ \frac{6.42}{8.025} \approx 0.80 \]
Thus, we have:
\[ \text{Number of years} \approx 0.80 \times 10^2 = 8.0 \times 10^1 \]
In scientific notation, we express \(0.80\) as \(8.0\) with an appropriate exponent adjustment:
\[ \text{Number of years} = 8 \times 10^1 \]
Therefore, the answer is:
\[ \boxed{8 \times 10^1} \]