When the decimal 0.36 is written as a fraction in its simplest (lowest terms) form, what is the sum of the numerator and the denominator of that fraction?

Introduction / Context:
This question checks your understanding of converting terminating decimals into fractions and then simplifying them to lowest terms. Such decimal-to-fraction conversions are common in aptitude tests and help reinforce the link between decimal notation and rational numbers.

Given Data / Assumptions:

• Decimal given: 0.36.
• We must express 0.36 as a fraction in simplest form.
• Then we must find the sum of the numerator and the denominator.

Concept / Approach:
A terminating decimal can be written as a fraction with a power of 10 in the denominator and the decimal digits as the numerator, and then simplified by dividing numerator and denominator by their greatest common divisor (GCD). Here 0.36 has two decimal places, so we first write it as 36/100 and then reduce the fraction to lowest terms.

Step-by-Step Solution:
Step 1: Write 0.36 as a fraction with denominator 100: 0.36 = 36/100. Step 2: Find the greatest common divisor of 36 and 100. Step 3: The prime factors of 36 are 2 * 2 * 3 * 3, and the prime factors of 100 are 2 * 2 * 5 * 5. The common factors are 2 * 2 = 4. Step 4: Divide numerator and denominator by 4: 36 ÷ 4 = 9, and 100 ÷ 4 = 25. Step 5: So 0.36 = 36/100 = 9/25 in simplest form. Step 6: Sum of numerator and denominator = 9 + 25 = 34.
Verification / Alternative check:
Convert 9/25 back to a decimal: 9 ÷ 25 = 0.36 exactly, so 9/25 is indeed equivalent to 0.36 and is fully simplified because 9 and 25 have no common factor other than 1.
Why Other Options Are Wrong:
15 might be obtained by incorrectly using 3/10 instead of 9/25 as the simplified fraction. 64 and 13 do not correspond to any correct pair of numerator and denominator representing 0.36 in lowest terms.
Common Pitfalls:
A frequent error is to stop at 36/100 without simplifying, or to divide by a smaller common factor like 2 or 5 instead of the full GCD 4. Another mistake is to miscalculate the GCD and obtain a fraction that still can be reduced further.
Final Answer:
The sum of the numerator and denominator is 34.