Evaluate the product 0.002 × 0.5 and express the result as a decimal.

Introduction / Context:
This is a basic decimal multiplication question and tests your understanding of how multiplying by a fraction less than 1 affects the value of a small decimal. Such problems appear in the fundamentals of decimal fractions, percentages, and measurement conversions.

Given Data / Assumptions:

• We need to compute 0.002 × 0.5.
• Both numbers are positive decimals.
• We want the exact decimal value of the product.
• No rounding is required, and all options are simple decimals.

Concept / Approach:
We recall that 0.5 is equal to 1/2. Multiplying a number by 1/2 is the same as taking half of that number. So this problem can be interpreted as finding half of 0.002. Alternatively, we can treat both numbers as decimals and multiply directly, keeping track of the total number of decimal places.

Step-by-Step Solution:
Interpret 0.5 as 1/2.Compute half of 0.002: 0.002 ÷ 2 = 0.001.Therefore, 0.002 × 0.5 = 0.001.We can also confirm by counting decimal places using direct multiplication.Write 0.002 as 2 × 10^-3 and 0.5 as 5 × 10^-1.Multiply: (2 × 10^-3) × (5 × 10^-1) = 10 × 10^-4 = 10^-3 = 0.001.Both methods lead to the same result.

Verification / Alternative check:
Another way is to convert to fractions. 0.002 = 2/1000 and 0.5 = 1/2. Multiply: (2/1000) × (1/2) = 2 / 2000 = 1 / 1000. The fraction 1 / 1000 corresponds to the decimal 0.001. This fraction based method confirms the decimal calculation and shows the consistency of the answer across different approaches.

Why Other Options Are Wrong:
Option 0.0001 is ten times smaller than the correct value and would correspond to mistakenly shifting the decimal one extra place to the left. Option 0.01 and 0.1 are significantly larger and reflect a misunderstanding that multiplying by 0.5 should make the number larger, which is not true. Option 0.00001 is even smaller and corresponds to two extra left shifts. Only 0.001 correctly represents half of 0.002.

Common Pitfalls:
Some students confuse multiplication by 0.5 with division by 0.5, which would double the number instead of halving it. Another mistake is miscounting decimal places when multiplying small decimals, often introducing one or more extra zeros. A useful habit is to interpret 0.5 as 1/2 and think in terms of taking half, which provides a strong intuitive check on the size of the final answer.

Final Answer:
The product 0.002 × 0.5 is equal to 0.001.