Compute the highest common factor (H.C.F.) of the decimals 0.54, 1.8, and 7.2.

Introduction / Context:
Finding the highest common factor (H.C.F.) of decimal numbers is easier if we remove decimals by scaling to integers, compute the integer H.C.F., and then scale back. This standard technique avoids repeated decimal operations.

Given Data / Assumptions:

• Numbers: 0.54, 1.8, 7.2.
• All are finite decimals with at most one or two decimal places.

Concept / Approach:
Multiply each number by 100 to clear decimals uniformly: 0.54 → 54, 1.8 → 180, 7.2 → 720. Compute H.C.F.(54, 180, 720), then divide by 100 to return to the original scale.

Step-by-Step Solution:
Scale: 0.54, 1.8, 7.2 → 54, 180, 720.H.C.F.(54, 180) = 18.H.C.F.(18, 720) = 18 (since 720 ÷ 18 = 40).Scale back by 100: 18 / 100 = 0.18.

Verification / Alternative check:
Divide each original number by 0.18: 0.54/0.18 = 3, 1.8/0.18 = 10, 7.2/0.18 = 40. All results are integers, so 0.18 is indeed a common factor. No larger decimal works because the corresponding integer H.C.F. is 18.

Why Other Options Are Wrong:
1.8 and 18: Too large when scaled back; do not divide 0.54 exactly..018: Too small; not the highest.0.9: Does not divide 0.54 exactly into an integer.

Common Pitfalls:
Forgetting to scale all numbers by the same power of 10; taking common factor but not the highest; mismanaging decimal places when scaling back.

Final Answer:
0.18