{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260923-real-terminating-decimal-fraction-0006", "pilot_number": "R0068-34931", "number": 34931, "family_id": "qf-real-terminating-decimal-fraction", "title": { "zh-Hant": "第 34931 題：有限小數的精確分數", "en": "Question 34931: Exact Fraction for a Terminating Decimal" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260923-real-terminating-decimal-fraction-0006", "batch_id": "batch-20260923-real-number-rational-points", "language": "zh-Hant", "source_mko_ids": [ "mko-real-number" ], "title_zh": "有限小數的精確分數", "stem_zh": "把明示十進位字串 -0.75 精確轉成最簡正分母分數；不得使用浮點近似。", "answer": { "kind": "short_text", "value": "-3/4", "explanation_zh": "-0.75 依小數位數轉為整數分子/10^k，再以 gcd 約成 -3/4。" }, "difficulty": { "band": "lower_secondary", "level": 1, "skills": [ "有限小數", "gcd" ] }, "variant": { "family_id": "qf-real-terminating-decimal-fraction", "seed": 20260929, "parameters": { "decimal": "-0.75", "scale": 2, "operation": "decimal_to_fraction", "semantic_template": "qf-real-terminating-decimal-fraction/{\"decimal\":\"-0.75\",\"operation\":\"decimal_to_fraction\",\"scale\":2}" } }, "verification": { "status": "candidate", "checks": [ "schema_pending", "independent_recomputation_pending" ], "warning_zh": "本題為 candidate 練習；有限精確重算不是形式證明或人工審查。" }, "provenance": { "generator_role": "question_producer", "generator_model": "GPT-5.6 Terra", "generated_at": "2026-09-23", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260923-real-terminating-decimal-fraction-0006", "batch_id": "batch-20260923-real-number-rational-points", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "7178ee2eaf952c3a0401f5ff3799b92cc1553669932eb7ac843d346f6c9796e1", "family_id": "qf-real-terminating-decimal-fraction", "seed": 20260929, "semantic_template": "qf-real-terminating-decimal-fraction/{\"decimal\":\"-0.75\",\"operation\":\"decimal_to_fraction\",\"scale\":2}" }, "fields": { "title": "Exact Fraction for a Terminating Decimal", "stem": "Convert the explicit decimal string -0.75 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.", "answer": { "kind": "short_text", "value": "-3/4", "explanation": "-0.75 is converted to an integer numerator over 10^2 and reduced by the gcd, giving -3/4." }, "skills": [ "terminating decimals", "gcd" ], "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review." } }, "givens": [ { "id": "G001", "text": { "zh-Hant": "把明示十進位字串 -0.75 精確轉成最簡正分母分數；不得使用浮點近似。", "en": "Convert the explicit decimal string -0.75 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation." } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-real-terminating-decimal-fraction, [decimal, operation, scale]]", "after": "derived = [decimal_to_fraction, no-invented-domain]", "relation": "implies", "rule_id": "R68_BANK_specific_keys_operations_and_numeric_guards", "conditions": [], "explanation": { "zh-Hant": "按來源分bank：legacy raw SAFE/衍生BigInt無界，BASE Number.isInteger不偷加SAFE/百萬界。underscore operation、domain及寬/嚴keys各依本bank；原JSON完整保存。", "en": "Separate source banks:legacy RAW SAFE with unbounded derived BigInts versus BASE Number.isInteger without invented SAFE/million caps.Operations,domains and permissive/exact keys follow THIS bank.Keep ORIGINAL JSON intact." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "Decimal ORIGINAL power10 place1 := mul(1, 10)", "after": "Decimal ORIGINAL power10 place1 = 10", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Decimal ORIGINAL power10 place1，不以小數近似替代。", "en": "Recompute Decimal ORIGINAL power10 place1 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "1", "10" ], "output": "10", "label": "Decimal ORIGINAL power10 place1" } }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "Decimal ORIGINAL power10 place2 := mul(10, 10)", "after": "Decimal ORIGINAL power10 place2 = 100", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Decimal ORIGINAL power10 place2，不以小數近似替代。", "en": "Recompute Decimal ORIGINAL power10 place2 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "10", "10" ], "output": "100", "label": "Decimal ORIGINAL power10 place2" } }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "Decimal ORIGINAL whole part times power10 := mul(0, 100)", "after": "Decimal ORIGINAL whole part times power10 = 0", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Decimal ORIGINAL whole part times power10，不以小數近似替代。", "en": "Recompute Decimal ORIGINAL whole part times power10 with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "0", "100" ], "output": "0", "label": "Decimal ORIGINAL whole part times power10" } }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "Decimal ORIGINAL add ALL fractional digits := sum(0, 75)", "after": "Decimal ORIGINAL add ALL fractional digits = 75", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Decimal ORIGINAL add ALL fractional digits，不以小數近似替代。", "en": "Recompute Decimal ORIGINAL add ALL fractional digits with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "sum", "inputs": [ "0", "75" ], "output": "75", "label": "Decimal ORIGINAL add ALL fractional digits" } }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "Decimal ORIGINAL apply explicit sign := mul(-1, 75)", "after": "Decimal ORIGINAL apply explicit sign = -75", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Decimal ORIGINAL apply explicit sign，不以小數近似替代。", "en": "Recompute Decimal ORIGINAL apply explicit sign with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "mul", "inputs": [ "-1", "75" ], "output": "-75", "label": "Decimal ORIGINAL apply explicit sign" } }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "source roles = [-0.75, 2, 0, 75]", "after": "derived = [-75, 100]", "relation": "implies", "rule_id": "Real_DECIMAL_lexical_places_EXACT_integer_over_power10", "conditions": [], "explanation": { "zh-Hant": "保留原字串與小數位數，整數部分*10^scale加全部小數digits再套符號；不經float解析，0.001的兩個前導小數0不能消掉scale。", "en": "Preserve the ORIGINAL string and place count.Compute whole*10^scale plus ALL fractional digits,then apply the sign,WITHOUT floating parsing.The leading fractional zeros in0.001 still count toward scale." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "Decimal exact derived fraction ORIGINAL exact numerator over nonzero denominator := div(-75, 100)", "after": "Decimal exact derived fraction ORIGINAL exact numerator over nonzero denominator = -3/4", "relation": "calculation", "rule_id": "exact_rational_arithmetic", "conditions": [], "explanation": { "zh-Hant": "按原操作數/次序精確運算；乘/減/除明示兩操作數，legacy BigInt衍生量不重套raw SAFE界，BASE Number來源的型別/表示條件另驗，不以浮點近似湊答案。", "en": "Calculate exactly from ORIGINAL ordered operands;mul/sub/div have EXPLICITLY TWO operands.Legacy derived BigInts are not recapped at RAW SAFE;check BASE Number type/representation conditions separately.Do not use floating approximations to force an answer." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "以精確有理數重算 Decimal exact derived fraction ORIGINAL exact numerator over nonzero denominator，不以小數近似替代。", "en": "Recompute Decimal exact derived fraction ORIGINAL exact numerator over nonzero denominator with exact rational arithmetic, not rounded decimals." } }, "arithmetic": { "operation": "div", "inputs": [ "-75", "100" ], "output": "-3/4", "label": "Decimal exact derived fraction ORIGINAL exact numerator over nonzero denominator" } }, { "id": "S009", "uses": [ "G001", "S008" ], "before": "source roles = [Decimal exact derived fraction, [-75, 100]]", "after": "derived = [[-3, 4], -3/4]", "relation": "implies", "rule_id": "Real_BASE_fraction_sign_gcd_normalization_NO_invented_SAFEcap", "conditions": [], "explanation": { "zh-Hant": "BASE normalizeFraction要整數num/den且den非0，不偷加SAFE/百萬/一億界。先正den再gcd約分，零為0/1；此衍生表示不改原raw pair。", "en": "BASE normalizeFraction requires INTEGER components and nonzero denominator,without invented SAFE/million/100million caps.Normalize denominator sign and gcd;zero is0/1.This derived representation does not alter the ORIGINAL raw pair." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反向核對本題的原始已知量、論域與本步條件；保留原題/英文/MKO/AST/狀態，不把單向推論倒成等價，也不把有限核對當獨立審查或一般形式證明。", "en": "Reverse-check THIS question’s ORIGINAL givens,domain and step premises.Preserve originals/English/MKOs/ASTs/status;do not reverse a one-way implication or call finite checks independent review or general formal proof." } }, "arithmetic": null } ], "math_model": { "result": "-3/4" }, "conclusion": { "canonical_value": "-3/4", "explanation": { "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。", "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged." } }, "definition_note": { "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。", "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate." }, "source": { "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db", "question_binding": { "batch_id": "batch-20260923-real-number-rational-points", "batch_path": "public/data/questions/batches/batch-20260923-real-number-rational-points/questions.jsonl", "batch_sha256": "d19b574fb612be66646603f4bbeec96578a1d948a33ab097ee9b84b2e171e5e9", "original_line": 6, "original_line_sha256": "793a59f16e197ef1acd083bf6718f0757fdd1c64aa1439d7f17d1e11ad5ddb92", "question_compact_sha256": "7178ee2eaf952c3a0401f5ff3799b92cc1553669932eb7ac843d346f6c9796e1", "english_row_compact_sha256": "87795df0581b5949a2bc2c7d853b06450d6f2fd01141ac2ef5f2e7184d542b53", "english_manifest_path": "public/data/i18n/editions/batch-20260923-real-number-rational-points.en.json", "english_rows_path": "public/data/i18n/questions/batch-20260923-real-number-rational-points.en.jsonl" }, "mko_bindings": { "mko-real-number": { "sha256": "2bc8c0a1defae2276ce50808a0761bf4d62f26892e443fcab79fc8090113d880", "english_sha256": "5dde700ff98e1ae0b35a5924253f8ad22515aa33c9a17deab8b7fa9a35e1ef5c", "original_path": "public/data/mko/real-number.json", "english_path": "public/data/i18n/editions/mko-real-number.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "345142be27643acca9d0fec2422ac7311b85bf142709391cd6b5b3a33c03cf8e", "original_candidate_sha256": "dbba06e0056c72380b17830c99049712569dc5bf865a3aa134855c3cccfb7654", "original_candidate_line_sha256": "dbba06e0056c72380b17830c99049712569dc5bf865a3aa134855c3cccfb7654" }, "historical_source_state": { "review_state": { "derivation": "candidate_authored_and_locally_checked", "source_question_state": "candidate", "independent_AI_or_human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN" }, "scope_note": { "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。", "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged." }, "label": "Frozen producer metadata; current per-question review is separate below." }, "revision": { "id": "review-20261026-012-p69", "review_date": "2026-10-26", "owner_authorized_reader_publication": true, "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.", "review_receipts": { "semantic_review_sha256": "e7a54104fa02c235f7591329bd6db8d626dd74bf0fae29c557b1f269c85066ed", "question_first_witness_sha256": "8401a3c2064c1275a6a7ea8f00412fa12286cec7b2db6c305ff9dba3724ae229" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 9, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "0db390d2dab136cfcf6288f78776d858422dacc0d3069ec99f44c6db5ae2c481", "arithmetic_steps": 6 }, "uses_answer_as_premise": false, "human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN", "Canonical_truth_promotion": false, "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged." } }