To multiply \( (9.42 \times 10^8) \cdot 250,000 \), we can first rewrite 250,000 in scientific notation:
\[ 250,000 = 2.5 \times 10^5 \]
Now we can perform the multiplication:
\[ (9.42 \times 10^8) \cdot (2.5 \times 10^5) \]
Using the properties of multiplication for numbers in scientific notation, we multiply the coefficients and add the exponents of the powers of 10:
\[ 9.42 \times 2.5 = 23.55 \]
For the powers of 10:
\[ 10^8 \cdot 10^5 = 10^{8 + 5} = 10^{13} \]
Putting it all together, we have:
\[ 23.55 \times 10^{13} \]
Now we need to express \( 23.55 \) in proper scientific notation. We can move the decimal one place to the left:
\[ 23.55 = 2.355 \times 10^1 \]
Now we can combine the two parts:
\[ (2.355 \times 10^1) \times 10^{13} = 2.355 \times 10^{1 + 13} = 2.355 \times 10^{14} \]
Thus, the answer in scientific notation is:
\[ \boxed{2.355 \times 10^{14}} \]
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