To solve the expression \( \frac{4.54 \times 10^4}{2.5 \times 10^3} \times (2.5 \times 10^{-2}) \), we can break it down step by step.
- First, simplify the fraction:
\[ \frac{4.54 \times 10^4}{2.5 \times 10^3} = \frac{4.54}{2.5} \times \frac{10^4}{10^3} = \frac{4.54}{2.5} \times 10^{4-3} = \frac{4.54}{2.5} \times 10^1 \]
Calculating \( \frac{4.54}{2.5} \):
\[ \frac{4.54}{2.5} = 1.816 \]
Now, multiplying by \( 10^1 \):
\[ 1.816 \times 10^1 = 18.16 \]
- Now multiply by \( (2.5 \times 10^{-2}) \):
\[ 18.16 \times (2.5 \times 10^{-2}) = 18.16 \times 2.5 \times 10^{-2} \]
Calculating \( 18.16 \times 2.5 \):
\[ 18.16 \times 2.5 = 45.4 \]
Now, multiplying by \( 10^{-2} \):
\[ 45.4 \times 10^{-2} = 0.454 \]
So the final value of the expression is:
\[ \boxed{0.454} \]