{
  "capability_id": "math.scientific_notation",
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  "engine": "scientific-notation",
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  "engine_build": "2026-09-21",
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  "failed": 0,
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      "passed": 4
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    "boundary": {
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    "property": {
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  "expert_reviewed": false,
  "internally_reviewed": false,
  "review_kind": null,
  "source_checked": true,
  "reviewed_by": null,
  "reviewer_role": null,
  "last_reviewed": null,
  "expert_review": {
    "status": "optional_not_performed",
    "reviewer": null,
    "scope": [
      "formula",
      "input semantics",
      "assumptions",
      "limitations",
      "sources",
      "tests"
    ],
    "note": "Domain expert review is optional under CVP (CVP-EXP-01). Absence does not block CVP Verified. See Review policy for supplemental domain assurance."
  },
  "internal_review": {
    "status": "not_applicable",
    "reviewer": null
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  "page": "https://www.calculatorx.com/calc/math/scientific-notation",
  "api": "https://www.calculatorx.com/api/v1/calc/scientific-notation",
  "schema_input": "https://www.calculatorx.com/schemas/math.scientific_notation.input.json",
  "schema_output": "https://www.calculatorx.com/schemas/math.scientific_notation.output.json",
  "assumptions": [
    "Finite IEEE-754 binary64 values. Inputs outside the supported floating-point range are rejected or reported as overflow/underflow. Very large/small in-range values use exponential display.",
    "UI, share URLs, REST, and validation cases all call this same engine."
  ],
  "limitations": [
    "Canonical Agent modes are convert / engineering / normalize / operate. dec-sci, sci-dec, numInput, coefInput, expInput, aInput, bInput are URL/engine adapter aliases, not the Agent contract.",
    "Missing/invalid numbers → INVALID_NUMBER / MISSING_REQUIRED_INPUT",
    "Division by zero in operate → DIVISION_BY_ZERO"
  ],
  "boundary_conditions": [
    "Division by zero rejected (DIVISION_BY_ZERO)",
    "Empty or unparsable input rejected (MISSING_REQUIRED_INPUT / INVALID_NUMBER)",
    "Inputs outside the IEEE-754 binary64 range rejected (RESULT_OVERFLOW / RESULT_UNDERFLOW)",
    "Zero is returned as 0, not A × 10ⁿ with 1 ≤ |A| < 10"
  ],
  "sources": [
    {
      "title": "OpenStax Elementary Algebra 2e — Scientific Notation",
      "section": "5.2 An application of exponents: scientific notation",
      "url": "https://openstax.org/books/elementary-algebra-2e/pages/5-2-an-application-of-exponents-scientific-notation",
      "supports": "A number in scientific notation is written A × 10ⁿ with 1 ≤ |A| < 10 and integer n; 0 is the exception",
      "kind": "reference",
      "accessed": "2026-08-30"
    },
    {
      "title": "BIPM SI Brochure (9th edition)",
      "section": "Table 8 — SI prefixes (powers of 10³)",
      "url": "https://www.bipm.org/en/publications/si-brochure",
      "supports": "Engineering notation uses exponents that are multiples of 3 so values line up with SI prefixes",
      "kind": "standard",
      "accessed": "2026-08-30"
    },
    {
      "title": "NIST SI prefixes",
      "section": "SI prefixes from 10⁻³⁰ to 10³⁰",
      "url": "https://www.nist.gov/pml/owm/metric-si-prefixes",
      "supports": "Prefix names (milli, micro, kilo, mega, …) attached to engineering exponents",
      "kind": "standard",
      "accessed": "2026-08-30"
    }
  ],
  "methods": [
    "IEEE-754 binary64 parse of decimal / E-notation / A×10ⁿ",
    "Normalize via Number#toExponential; engineering exponent ≡ 0 (mod 3)",
    "Test suites are not interchangeable: 20 published examples on this page · 124 automated engine checks (IUT) · CVP verification suite on Evidence (Manifest is the verification source of truth)"
  ],
  "fingerprint": "sha256:79247c5984f5620b9ef17a07db08f7fdd75ab6ca22af81c141e7b444cc23c9b9",
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        "value": 12300
      },
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        "coef": 1.23,
        "exp": 4
      },
      "expectWarning": null,
      "actual": {
        "mode": "convert",
        "calculation_version": "2.0.0",
        "heading": "Scientific notation",
        "value": "1.23 × 10⁴",
        "scientific": "1.23 × 10⁴",
        "e_notation": "1.23e4",
        "engineering": "12.3 × 10³",
        "decimal": "12300",
        "order": 4,
        "si": "kilo (k)",
        "coef": 1.23,
        "exp": 4,
        "eng_coef": 12.3,
        "eng_exp": 3,
        "parsed": 12300,
        "input": "12300",
        "inputs_summary": "12300",
        "mode_label": "Convert",
        "formula": "x = A × 10ⁿ, 1 ≤ |A| < 10, for x ≠ 0",
        "explainer": "1.23e4 · eng 12.3 × 10³ · order 4",
        "steps": [
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          "Parsed value: 12300",
          "Scientific: 1.23 × 10⁴   (1 ≤ |A| < 10)",
          "E-notation: 1.23e4",
          "Engineering: 12.3 × 10³   · SI: kilo (k)",
          "Order of magnitude: 4",
          "Real / standard: 12300",
          "Decimal shift: move point 4 place(s) left to get 1.23."
        ],
        "equivalents": [
          [
            "Scientific",
            "1.23 × 10⁴"
          ],
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            "E notation",
            "1.23e4"
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            "12.3 × 10³"
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            "12300"
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      },
      "tol": 1e-12
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    {
      "id": "convert-1",
      "ok": true,
      "kind": "golden",
      "inputs": {
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      },
      "expect": {
        "coef": 1,
        "exp": 0
      },
      "expectWarning": null,
      "actual": {
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        "scientific": "1 × 10⁰",
        "e_notation": "1e0",
        "engineering": "1 × 10⁰",
        "decimal": "1",
        "order": 0,
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        "coef": 1,
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        "inputs_summary": "1",
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          "Parsed value: 1",
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          "E-notation: 1e0",
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          "Real / standard: 1"
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        "equivalents": [
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            "E notation",
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      "tol": 0
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      "kind": "golden",
      "inputs": {
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      "expectWarning": null,
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        "coef": 0,
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