1. **State the problem:** Calculate the value of the expression $0.14 - \frac{0.059}{2} \log_{10} 125$. 2. **Recall the formula and rules:** - The logarithm base 10 of 125 can be simplified using properties of logarithms. - $\log_{10} 125 = \log_{10} (5^3) = 3 \log_{10} 5$. - We know $\log_{10} 5 \approx 0.69897$. 3. **Calculate $\log_{10} 125$:** $$\log_{10} 125 = 3 \times 0.69897 = 2.09691$$ 4. **Calculate the division part:** $$\frac{0.059}{2} = 0.0295$$ 5. **Multiply the division result by the logarithm:** $$0.0295 \times 2.09691 \approx 0.0618$$ 6. **Subtract from 0.14:** $$0.14 - 0.0618 = 0.0782$$ **Final answer:** $$\boxed{0.0782}$$