Substitute the values: \( s = 0 \times 10 + \frac{1}{2} \times 3 \times 10^2 \).
["Understanding Substitutions: Evaluating the Expression ( s = 0 \ imes 10 + \frac{1}{2} \ imes 3 \ imes 10^2 )", "When working with mathematical expressions, substitution plays a fundamental role in simplifying calculations and clarifying complex formulas. One classic example is evaluating the expression:", "[\ns = 0 \ imes 10 + \frac{1}{2} \ imes 3 \ imes 10^2\n]", "At first glance, substituting values directly may feel mechanical—but understanding the correct substitution and order of operations is essential for accuracy and deeper comprehension.", "### Step-by-step Substitution and Evaluation", "Step 1: Identify Substituted Values\nHere, no numerical constants are explicitly "substituted"—but they are embedded through operations:", "- ( 0 ) and ( 10 ) are explicitly substituted into the first term: ( 0 \ imes 10 )\n- ( 3 ) and ( 10^2 ) are substituted into the second term: ( \frac{1}{2} \ imes 3 \ imes 10^2 )", "However, logical substitution raises an important point: what if variables represent unknown quantities? In real applications, mathematical expressions often contain variables whose values must be substituted before computation. In this case, even though values are numerically given, substituting them correctly ensures alignment with algebraic rules.", "---", "### Breaking Down the Expression", "Evaluate each term using proper order of operations (PEMDAS/BODMAS):", "First Term:\n[\n0 \ imes 10 = 0\n]", "Second Term:\n[\n\frac{1}{2} \ imes 3 \ imes 10^2 = \frac{1}{2} \ imes 3 \ imes 100\n]\nまず:\n[\n3 \ imes 100 = 300\n]\nOr Alternatively:\n[\n\frac{1}{2} \ imes 300 = 150\n]", "---", "### Final Calculation", "Add both terms:\n[\ns = 0 + 150 = 150\n]", "### Conclusion", "The fully evaluated expression is:\n[\n\boxed{s = 150}\n]", "### Why Substitution Matters in Mathematics", "Substituting values—or clearly defining variables—ensures precision and avoids ambiguity. In educational contexts, modeling substitution reinforces logical thinking and problem-solving skills. In programming and scientific computing, accurate substitution prevents logical errors that can lead to incorrect results.", "---", "Key Takeaways:\n- Always apply mathematical operations in correct order: parentheses first, then exponents, multiplication/division, addition/subtraction.\n- Substitution isn’t always about balancing digits—it may involve clarity of defined values.\n- Expressions like ( s = 0 \ imes 10 + \frac{1}{2} \ imes 3 \ imes 10^2 ) demonstrate how substitution enables simplification into measurable results.", "By mastering substitution and evaluation, students and professionals alike enhance both computational accuracy and conceptual understanding in algebra and beyond."]
