1. The problem asks us to compare $12.5 \times 10^{-4}$ and $1.25 \times 10^{-3}$. 2. Both numbers are in scientific notation, which is expressed as $a \times 10^n$ where $a$ is the coefficient and $n$ is the exponent. 3. To compare, convert both to the same power of ten or to decimal form. 4. Convert $12.5 \times 10^{-4}$ to decimal: $$12.5 \times 10^{-4} = 12.5 \times 0.0001 = 0.00125$$ 5. Convert $1.25 \times 10^{-3}$ to decimal: $$1.25 \times 10^{-3} = 1.25 \times 0.001 = 0.00125$$ 6. Both values equal $0.00125$, so they are equal. 7. Therefore, $12.5 \times 10^{-4} = 1.25 \times 10^{-3}$.