Decimals with chained multiplication and division Evaluate 0.01 × 0.3 ÷ 0.4 × 0.5 (use left-to-right precedence for multiplication/division).

Introduction / Context:Chained decimal operations require attention to both decimal placement and operation order. Multiplication and division share the same precedence and are evaluated from left to right.

Given Data / Assumptions:

• Expression: 0.01 × 0.3 ÷ 0.4 × 0.5.
• Left-to-right evaluation for × and ÷.

Concept / Approach:Compute sequentially: first multiply 0.01 by 0.3, then divide the result by 0.4, then multiply by 0.5. Convert divisions by decimals into multiplications by reciprocals if helpful.

Step-by-Step Solution:First: 0.01 × 0.3 = 0.003.Second: 0.003 ÷ 0.4 = 0.003 / 0.4 = 0.0075.Third: 0.0075 × 0.5 = 0.00375.

Verification / Alternative check:As fractions: 0.01 = 1/100; 0.3 = 3/10; 0.4 = 2/5; 0.5 = 1/2. Product = (1/100)*(3/10)/(2/5)*(1/2) = (3/1000)*(5/2)*(1/2) = 15/4000 = 3/800 = 0.00375.

Why Other Options Are Wrong:.015 and .0375 arise from skipping the division by 0.4 or mis-ordering steps; .1 is far too large; .0125 corresponds to partial computation errors.

Common Pitfalls:Applying right-to-left instead of left-to-right for same-precedence operations; decimal point misplacement during division by 0.4.

Final Answer:.00375