Convert the terminating decimal 0.2341 into a fraction p/q in lowest terms, where p and q are integers and q ≠ 0.

Introduction / Context:
Terminating decimals convert cleanly to fractions by placing the digits over an appropriate power of 10 and then reducing if possible. Recognizing when a decimal terminates is the key first step.

Given Data / Assumptions:

• Decimal: 0.2341.
• It has four digits after the decimal point.

Concept / Approach:
A decimal with four places equals an integer divided by 10^4. Therefore, 0.2341 = 2341/10000. If the numerator and denominator share a common factor, reduce to lowest terms; otherwise, the fraction is already simplified.

Step-by-Step Solution:
Write 0.2341 as 2341/10000 (since there are four decimal places).Check simplification: 2341 is not divisible by 2 or 5, and quick divisibility checks for small primes (3, 7, 11, 13) fail.Thus, the fraction 2341/10000 is already in lowest terms.

Verification / Alternative check:
Convert back to decimal: 2341/10000 = 0.2341 exactly, confirming correctness.

Why Other Options Are Wrong:
2341/9990, 2339/9990, 781/3330, 11705/50000: These correspond to non-terminating (repeating) or mismatched decimals and do not equal 0.2341 exactly.

Common Pitfalls:
Confusing terminating decimals with repeating ones; using 999… denominators unnecessarily; attempting to reduce by 2 or 5 when the numerator is not divisible by these factors.

Final Answer:
2341/10000