Convert the recurring decimal 0.232323… into a fraction in lowest terms.

Problem restatementExpress 0.232323… (repeating block 23) as a rational fraction.

Concept/ApproachIf x = 0.232323…, then 100x = 23.232323…; subtract x to eliminate the repeating part.

Step-by-Step calculationLet x = 0.232323…100x = 23.232323…99x = 23x = 23 / 9923/99

Verification/Alternative23/99 = (0.23)/(0.99) ≈ 0.232323…; irreducible since 23 is prime and does not divide 99.

Common pitfallsWriting 23/90 (incorrect denominator for a two-digit repetend; it must be 99).

Final Answer23/99