Find the greatest common divisor (G.C.D.) of the decimal numbers 1.08, 0.36 and 0.9.

Introduction / Context:
This question tests your understanding of finding the greatest common divisor (G.C.D., also known as H.C.F.) when the numbers are given in decimal form. Converting decimals into whole numbers by using a common factor of 10 is a standard strategy. Such problems appear in aptitude tests to examine your comfort with decimals and factors together.

Given Data / Assumptions:

• The numbers are 1.08, 0.36, and 0.9.
• We are asked to determine their greatest common divisor.
• All numbers are positive decimal numbers.

Concept / Approach:
To find the G.C.D. of decimal numbers, we can scale them by a power of 10 so that all numbers become integers. We then compute the G.C.D. of these integers and finally scale back by dividing by the same power of 10. This makes the calculation much easier and avoids confusion with decimal arithmetic.

Step-by-Step Solution:
Step 1: Express each decimal with two decimal places: 1.08, 0.36, and 0.90.Step 2: Multiply each by 100 to remove decimals: 1.08 * 100 = 108, 0.36 * 100 = 36, 0.9 * 100 = 90.Step 3: Now find the G.C.D. of the integers 108, 36, and 90.Step 4: First, gcd(108, 36) = 36, because 36 divides 108 exactly.Step 5: Next, gcd(36, 90) = 18.Step 6: So the G.C.D. of 108, 36, and 90 is 18.Step 7: Since we multiplied by 100 earlier, we now divide the G.C.D. by 100: 18 / 100 = 0.18.Step 8: Therefore, the greatest common divisor of 1.08, 0.36, and 0.9 is 0.18.

Verification / Alternative check:
Check divisibility: 1.08 ÷ 0.18 = 6, 0.36 ÷ 0.18 = 2, and 0.9 ÷ 0.18 = 5. All quotients are integers, confirming that 0.18 is a common divisor. No larger decimal (greater than 0.18) divides all three numbers exactly, so this is indeed the greatest common divisor.

Why Other Options Are Wrong:
Option a (0.03) is a common divisor but not the greatest, since 0.18 is larger and still divides all numbers. Option b (0.9) fails because 0.9 does not divide 1.08 or 0.36 exactly. Option d (0.108) does not divide 0.9 exactly into an integer quotient. Therefore these options cannot represent the G.C.D.

Common Pitfalls:
Some students attempt to work directly with decimals and make arithmetic mistakes. Others forget to apply the same scaling factor to all numbers. A reliable technique is to convert all decimals to integers using a common power of 10, compute the G.C.D. of the integers, and then scale back to obtain the final answer in decimal form.

Final Answer:
The greatest common divisor of the three decimals is 0.18.