{
  "schema_version": "decimal-hours-precision/v1",
  "version": "1.0.0",
  "published_date": "2026-10-29",
  "owner": "Time Calculator",
  "canonical_page": "https://time-calculator.dev/minutes-to-decimal-chart",
  "scope": "Every integer second from 0 through 86400 inclusive; nonnegative elapsed durations, not clock readings",
  "rounding": "Nearest, exact halves upward (half away from zero on this nonnegative corpus); recover to nearest whole second using the same rule",
  "arithmetic": "Python integers and fractions.Fraction; no binary floating-point in the reference calculation",
  "total_comparisons": 259203,
  "results": [
    {
      "decimal_places": 2,
      "tested_durations": 86401,
      "quantum_seconds_fraction": "36",
      "max_absolute_display_error_seconds_fraction": "18",
      "first_max_error_input_seconds": 18,
      "exact_display_count": 2401,
      "changed_round_trips": 84000,
      "max_absolute_round_trip_error_seconds": 18
    },
    {
      "decimal_places": 3,
      "tested_durations": 86401,
      "quantum_seconds_fraction": "18/5",
      "max_absolute_display_error_seconds_fraction": "9/5",
      "first_max_error_input_seconds": 9,
      "exact_display_count": 4801,
      "changed_round_trips": 62400,
      "max_absolute_round_trip_error_seconds": 2
    },
    {
      "decimal_places": 4,
      "tested_durations": 86401,
      "quantum_seconds_fraction": "9/25",
      "max_absolute_display_error_seconds_fraction": "4/25",
      "first_max_error_input_seconds": 2,
      "exact_display_count": 9601,
      "changed_round_trips": 0,
      "max_absolute_round_trip_error_seconds": 0
    }
  ],
  "aggregation_examples": [
    {
      "entries": 3,
      "seconds_per_entry": 1200,
      "decimal_places": 2,
      "sum_of_rounded_hours": "0.99",
      "rounded_sum_hours": "1.00",
      "difference_seconds": -36
    },
    {
      "entries": 30,
      "seconds_per_entry": 60,
      "decimal_places": 4,
      "sum_of_rounded_hours": "0.5010",
      "rounded_sum_hours": "0.5000",
      "difference_seconds_fraction": "18/5"
    }
  ],
  "limitations": [
    "This is a deterministic arithmetic enumeration, not an empirical survey or a benchmark of third-party software.",
    "Excludes negative and subsecond inputs, durations beyond 24 hours, parsing, floating-point implementations, timezone, daylight-saving and payroll rounding policies.",
    "Zero changed four-place round trips is only a single-value nearest-second result on the stated corpus; it does not imply exact decimal values or exact sums."
  ],
  "reuse": "CC0-1.0 for original code and generated data; external publications retain their rights"
}