ROUND takes ties away from zero on the 15-digit reading, so 1.005 rounds up

FN-ROUND-004: ROUND takes ties away from zero on the 15-digit reading, so 1.005 rounds up

Excel differs from the mathematical answer · measured · recorded 2026-11-04

A tie in ROUND goes away from zero, not to even: ROUND(2.5,0) is 3 and ROUND(-2.5,0) is -3. The tie is judged on the 15-digit reading of FN-ROUND-002, not on the stored value. So 1.005 and 2.675, whose binary64 values lie just below the decimal tie, count as ties: ROUND(1.005,2) is 1.01 and ROUND(2.675,2) is 2.68, where rounding the stored value would give 1 and 2.67.

Correct value: The stored value lies below the decimal tie, so the nearest multiple of 0.01 is the lower one; nearest binary64.

Correct value: The stored value lies below the decimal tie, so the nearest multiple of 0.01 is the lower one; nearest binary64.

Basis: The readings below, typed as literals, and the family rule of FN-ROUND-002 over the recorded ROUND rows.

Inferred: That every tie follows this is inferred from the rule's fit to the recorded rows; the literal ties read directly are the ones below.