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:
\[
\text{Years} = \frac{\text{Total Interest}}{\text{Interest per Year}}
\]
In this case:
- Total Interest = \( 6.42 \times 10^4 \)
- Interest per Year = \( 802.50 \)
Now we can calculate the number of years:
\[
\text{Years} = \frac{6.42 \times 10^4}{802.50}
\]
Calculating the division:
1. First, we can convert \( 802.50 \) into scientific notation:
\( 802.50 = 8.025 \times 10^2 \)
2. Now, we can perform the division:
\[
\text{Years} = \frac{6.42 \times 10^4}{8.025 \times 10^2}
\]
3. Dividing the coefficients and subtracting the exponents gives:
\[
\text{Years} = \frac{6.42}{8.025} \times 10^{4-2} \approx 0.800 \times 10^2
\]
4. Converting \( 0.800 \) into proper scientific notation gives:
\[
\text{Years} \approx 8.00 \times 10^1
\]
Thus, the number of years it will take to yield \( 6.42 \times 10^4 \) dollars in interest is:
\[
\boxed{8 \times 10^1}
\]