Decimal multiplication fundamentals Compute the product: 0.9 × 0.008 = ?

Introduction / Context:
This problem checks fluency with multiplying decimal fractions. Knowing how to count decimal places and manage powers of 10 is essential for quick, accurate arithmetic in aptitude exams and daily calculations.

Given Data / Assumptions:

• Compute 0.9 * 0.008.
• All numbers are base-10 decimals.
• No rounding is required because the product is exact.

Concept / Approach:
Convert decimals into powers of 10 or count total decimal places. Specifically, 0.9 = 9/10 and 0.008 = 8/1000. Multiplying fractions (or multiplying the integers and adding decimal places) yields the exact result efficiently.

Step-by-Step Solution:
Rewrite 0.9 as 9/10.Rewrite 0.008 as 8/1000.Multiply: (9/10) * (8/1000) = 72/10000.Convert back to decimal: 72/10000 = 0.0072.

Verification / Alternative check:
As decimals, 0.9 has 1 decimal place and 0.008 has 3 decimal places; total 4 decimal places in the product of 9 * 8 = 72, leading to 0.0072. This cross-check matches the fraction method.

Why Other Options Are Wrong:
0.072: Off by one decimal place; implies only 3 total decimal places.0.00072: Off by one more decimal place; implies 5 places instead of 4.0.72: Ignores decimal scaling entirely.

Common Pitfalls:
Forgetting to add the total number of decimal places from both factors; multiplying 9 and 8 correctly but placing the decimal incorrectly. Always add decimal places or use fraction representation to avoid slips.

Final Answer:
0.0072