The simplified value of $ 0.002 imes 0.5 $ is:

Question

The simplified value of $ 0.002 	imes 0.5 $ is:

Examoogle · Accepted Answer

The correct answer is Option D: 0.001. Multiply the non-zero digits ($2 	imes 5 = 10$) and count the total number of decimal places in both numbers ($3 + 1 = 4$), then place the decimal point 4 places from the right.

Step-by-Step Solution & Concepts:
Shortcut Trick: Multiply the non-zero digits ($2 	imes 5 = 10$) and count the total number of decimal places in both numbers ($3 + 1 = 4$), then place the decimal point 4 places from the right.

Formula Used: $$0.002 	imes 0.5 = \frac{2}{1000} 	imes \frac{5}{10} = \frac{10}{10000} = 0.001$$

Given: Two decimal numbers: $0.002$ and $0.5$

Steps: Convert to Fractions: Express both decimal numbers as fractions of powers of 10. Here, $0.002 = \frac{2}{1000}$ and $0.5 = \frac{5}{10}$.. Multiply Fractions: Multiply the numerators together and the denominators together: $\frac{2 	imes 5}{1000 	imes 10} = \frac{10}{10000}$.. Simplify and Convert Back to Decimal: Cancel one zero from numerator and denominator to get $\frac{1}{1000}$, which equals $0.001$.

Answer: D is correct because multiplying $0.002$ by $0.5$ yields $0.001$.

Exam Tip: Counting decimal places is a fundamental shortcut used extensively in scientific notation and percentage calculations across quantitative aptitude tests.

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