Compute the GCD (HCF) of decimal numbers by clearing decimals: GCD of 1.08, 0.36, and 0.90. Demonstrate exact integer reduction.

Introduction / Context:To find the greatest common divisor (GCD) of decimals exactly, convert them to integers by multiplying with a common power of ten, compute the GCD of the integers, and then scale back. This avoids rounding and ensures correctness.

Given Data / Assumptions:

• Decimals: 1.08, 0.36, 0.90
• Use a common factor of 100 to clear two decimal places.

Concept / Approach:Multiply by 100: 1.08 → 108, 0.36 → 36, 0.90 → 90. Compute GCD(108, 36, 90). Then divide the GCD by 100 to return to decimal scale.

Step-by-Step Solution:GCD(108, 36) = 36.GCD(36, 90) = 18.So the scaled GCD is 18. Scale back: 18 ÷ 100 = 0.18.

Verification / Alternative check:Confirm divisibility: 1.08 ÷ 0.18 = 6; 0.36 ÷ 0.18 = 2; 0.90 ÷ 0.18 = 5. All are integers, confirming 0.18 divides each exactly.

Why Other Options Are Wrong:

• 0.108, 0.06, 0.03: Each divides some but not all of the numbers evenly.
• 0.9: Larger than some inputs; not a common divisor of 0.36.

Common Pitfalls:Scaling only some numbers or scaling back incorrectly; using approximate decimal GCDs without exact reduction.

Final Answer:0.18