The G.C.D. of $1.08$, $0.36$ and $0.9$ is

### Concept & Strategy The Greatest Common Divisor (GCD) is the exact same concept as the Highest Common Factor (HCF). To evaluate decimals, first equalize the number of decimal places across all terms, multiply by a base of $10$ to make them integers, find the GCD of those integers, and finally restore the decimal point. ### Step-by-Step Solution * **Given:** $1.08$, $0.36$, and $0.9$. * **Step 1: Equalize decimal places.** The maximum decimal places is two. Rewrite them as: $1.08$, $0.36$, $0.90$ * **Step 2: Remove decimals (Multiply by 100).** The numbers become $108$, $36$, and $90$. * **Step 3: Calculate GCD of $(108, 36, 90)$.** Notice that $36 \times 3 = 108$. So the GCD of $108$ and $36$ is just $36$. Now, find the GCD of $36$ and $90$. $36 = 18 \times 2$ $90 = 18 \times 5$ The highest common factor is clearly $18$. * **Step 4: Restore the decimal point.** Divide the result by the multiplier ($100$): $$18 \div 100 = 0.18$$ ### Exam Strategy & Shortcut Convert in your head: $108, 36, 90$. You know $18$ is a massive common factor here ($18 \times 6$, $18 \times 2$, $18 \times 5$). Since $2, 6, 5$ share no common factors, $18$ is the GCD. Divide by $100$ to get $0.18$. This takes less than 15 seconds if you are well-versed in your $18$ times table. ### Common Pitfall A frequent error is omitting the zero in $0.90$. Students often treat $0.9$ as just $9$ when converting, finding the GCD of $108, 36, 9$ (which is $9$), leading to an incorrect answer of $0.09$. Always pad with zeros to match the longest decimal before converting to integers. ### Final Answer **Therefore, the correct answer is 0.18.**