Question 34941: Exact Fraction for a Terminating Decimal

Original question and givens

Convert the explicit decimal string 0.09 exactly to a lowest-terms fraction with a positive denominator; do not use floating-point approximation.

• G001 — Convert the explicit decimal string 0.09 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.

• mko-real-number

Step-by-step derivation

source roles = [qf-real-terminating-decimal-fraction, [decimal, operation, scale]]

derived = [decimal_to_fraction, no-invented-domain]

Decimal ORIGINAL power10 place1 := mul(1, 10)

Decimal ORIGINAL power10 place1 = 10

Decimal ORIGINAL power10 place2 := mul(10, 10)

Decimal ORIGINAL power10 place2 = 100

Decimal ORIGINAL whole part times power10 := mul(0, 100)

Decimal ORIGINAL whole part times power10 = 0

Decimal ORIGINAL add ALL fractional digits := sum(0, 9)

Decimal ORIGINAL add ALL fractional digits = 9

Decimal ORIGINAL apply explicit sign := mul(1, 9)

Decimal ORIGINAL apply explicit sign = 9

source roles = [0.09, 2, 0, 09]

derived = [9, 100]

Decimal exact derived fraction ORIGINAL exact numerator over nonzero denominator := div(9, 100)

Decimal exact derived fraction ORIGINAL exact numerator over nonzero denominator = 9/100

source roles = [Decimal exact derived fraction, [9, 100]]

derived = [[9, 100], 9/100]

Reverse checks

• S009 · 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.
• S008 · premise_and_result_audit — Recompute Decimal exact derived fraction ORIGINAL exact numerator over nonzero denominator with exact rational arithmetic, not rounded decimals.
• S007 · 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.
• S006 · premise_and_result_audit — Recompute Decimal ORIGINAL apply explicit sign with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Recompute Decimal ORIGINAL add ALL fractional digits with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Recompute Decimal ORIGINAL whole part times power10 with exact rational arithmetic, not rounded decimals.
• S003 · premise_and_result_audit — Recompute Decimal ORIGINAL power10 place2 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

9/100

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.