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

Introduction / Context:
Decimals and fractions are two different ways of representing the same rational number. Competitive exams often test your ability to convert between these forms and then perform small operations like adding numerator and denominator. Here we work with the decimal 0.36 and convert it into a fraction in simplest form, then find the sum of its numerator and denominator.

Given Data / Assumptions:

• The given decimal is 0.36.
• We must express 0.36 as a fraction in simplest (lowest) terms.
• After simplification, we must add the numerator and the denominator.

Concept / Approach:
A terminating decimal can be converted into a fraction by writing it over a power of 10 and simplifying. For two decimal places, we use 100 as the denominator. Then we reduce the fraction by dividing numerator and denominator by their greatest common divisor (GCD). Finally, we add numerator and denominator to get the required sum.

Step-by-Step Solution:
Step 1: Write 0.36 as a fraction: 0.36 = 36 / 100. Step 2: Find common factors of 36 and 100. The GCD of 36 and 100 is 4. Step 3: Divide numerator and denominator by 4: 36 / 4 = 9 and 100 / 4 = 25. Step 4: So, 0.36 in simplest form is 9 / 25. Step 5: Now add the numerator and denominator: 9 + 25 = 34.

Verification / Alternative check:
We can convert 9 / 25 back to a decimal to confirm. Divide 9 by 25: 9 ÷ 25 = 0.36. Since this matches the original decimal, the fraction 9 / 25 is correct. The sum 9 + 25 = 34 is therefore reliable.

Why Other Options Are Wrong:
15: This would correspond to some incorrect simplified fraction such as 7 / 8 (7 + 8 = 15), which does not equal 0.36.
64: This would suggest a very different numerator and denominator, not matching 0.36.
13: This is too small to be the sum of numerator and denominator of 0.36 in simplest form.
49: Also does not relate to 9 / 25 and is just a distractor value.

Common Pitfalls:
A common mistake is to forget to simplify 36 / 100 and directly add 36 + 100 = 136, which is wrong. Another error is to reduce the fraction incorrectly by dividing by a number that is not the true GCD, leading to a non-simplest form. Always check divisibility carefully.

Final Answer:
The simplified fraction is 9 / 25 and the required sum of numerator and denominator is 34.