When the decimal 0.46 is written as a fraction in simplest form, what is the sum of the numerator and denominator?

Introduction / Context:
Here you are asked to convert a decimal into its simplest fraction form and then compute the sum of the numerator and denominator. This type of question checks both conversion skills and your ability to simplify fractions correctly.

Given Data / Assumptions:

• Decimal given: 0.46.
• We must convert 0.46 to a fraction and simplify it.
• Finally, we add the numerator and denominator of the simplified fraction.

Concept / Approach:
A decimal with two places can be written as a fraction over 100. Then we reduce this fraction by dividing numerator and denominator by their greatest common divisor. After finding the simplest fraction, we add its numerator and denominator to answer the question.

Step-by-Step Solution:
Step 1: Write 0.46 as a fraction with denominator 100. Since there are two decimal places, 0.46 = 46/100. Step 2: Find the greatest common divisor of 46 and 100. Both are divisible by 2. Step 3: Divide numerator and denominator by 2: 46 / 2 = 23 and 100 / 2 = 50. Step 4: The simplest form of 0.46 is therefore 23/50. Step 5: Now add the numerator and denominator: 23 + 50 = 73.

Verification / Alternative check:
To verify that 23/50 is correct, convert it back to decimal. Compute 23 ÷ 50. Multiply numerator and denominator by 2 to see that 23/50 = 46/100, which is 0.46. This confirms that our simplified fraction is correct and that the sum of numerator and denominator is indeed 73.

Why Other Options Are Wrong:
69 would require a different pair of numerator and denominator such as 19/50, which does not equal 0.46.
96 might come from miscalculations such as 46 + 50 or incorrect simplification steps.
41 could arise if someone incorrectly simplified 46/100 to 21/20 or another wrong fraction, which does not match 0.46.

Common Pitfalls:
Some learners attempt to cancel by 5 or 10 first and stop early, not reaching the simplest fraction. Others may mistakenly write 0.46 as 46/1000. Always match the decimal places to the correct power of 10 and then reduce by the largest common factor. Double check by converting back to decimal if unsure.

Final Answer:
The sum of the numerator and denominator in simplest form is 73.