Convert the explicit decimal string 12.5 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
G001 — Convert the explicit decimal string 12.5 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.
Definition and scope
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.
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.
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.
Decimal ORIGINAL whole part times power10 := mul(12, 10)
After
Decimal ORIGINAL whole part times power10 = 120
Conditions: none
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.
Decimal ORIGINAL add ALL fractional digits := sum(120, 5)
After
Decimal ORIGINAL add ALL fractional digits = 125
Conditions: none
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.
Decimal ORIGINAL apply explicit sign := mul(1, 125)
After
Decimal ORIGINAL apply explicit sign = 125
Conditions: none
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.
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.
Decimal exact derived fraction ORIGINAL exact numerator over nonzero denominator := div(125, 10)
After
Decimal exact derived fraction ORIGINAL exact numerator over nonzero denominator = 25/2
Conditions: none
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.
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.
S008 · premise_and_result_audit — 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.
S007 · premise_and_result_audit — Recompute Decimal exact derived fraction ORIGINAL exact numerator over nonzero denominator with exact rational arithmetic, not rounded decimals.
S006 · premise_and_result_audit — 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.
S005 · premise_and_result_audit — Recompute Decimal ORIGINAL apply explicit sign with exact rational arithmetic, not rounded decimals.
S004 · premise_and_result_audit — Recompute Decimal ORIGINAL add ALL fractional digits with exact rational arithmetic, not rounded decimals.
S003 · premise_and_result_audit — Recompute Decimal ORIGINAL whole part times power10 with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Recompute Decimal ORIGINAL power10 place1 with exact rational arithmetic, not rounded decimals.
S001 · premise_and_result_audit — 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.
Result
25/2
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.