{
    "name": "Scientific Notation Calculator",
    "url": "https://calculators.geekmidst.com/calculators/scientific-notation-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/scientific-notation-calculator.md",
    "category": "Mathematics",
    "description": "Convert numbers to scientific, E and engineering notation, or add, subtract, multiply and divide in scientific notation with significant figures.",
    "summary": "Scientific notation writes a number as a coefficient from 1 to under 10 times a power of ten, such as 4.56 × 10⁻⁴. It keeps very large and very small numbers readable.",
    "also_called": [
        "Standard form calculator",
        "Exponential notation converter"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "mode",
            "label": "Task",
            "type": "segmented",
            "default": "convert",
            "options": {
                "convert": "Convert a number",
                "calc": "Calculate"
            }
        },
        {
            "name": "number",
            "label": "Number",
            "type": "text",
            "default": "0.000456",
            "shown_when": {
                "mode": "convert"
            }
        },
        {
            "name": "a",
            "label": "First number",
            "type": "text",
            "default": "3e8",
            "shown_when": {
                "mode": "calc"
            }
        },
        {
            "name": "op",
            "label": "Operation",
            "type": "select",
            "default": "mul",
            "options": {
                "add": "Add (+)",
                "sub": "Subtract (−)",
                "mul": "Multiply (×)",
                "div": "Divide (÷)"
            },
            "shown_when": {
                "mode": "calc"
            }
        },
        {
            "name": "b",
            "label": "Second number",
            "type": "text",
            "default": "2e-3",
            "shown_when": {
                "mode": "calc"
            }
        },
        {
            "name": "sig",
            "label": "Significant figures",
            "type": "number",
            "default": "",
            "optional": true
        }
    ],
    "outputs": [
        {
            "key": "scientific",
            "label": "Scientific notation",
            "format": "text"
        },
        {
            "key": "e_notation",
            "label": "E notation",
            "format": "text"
        },
        {
            "key": "engineering",
            "label": "Engineering notation",
            "format": "text"
        },
        {
            "key": "decimal",
            "label": "Decimal form",
            "format": "text"
        },
        {
            "key": "coefficient",
            "label": "Coefficient",
            "format": "text"
        },
        {
            "key": "exponent",
            "label": "Exponent",
            "format": "integer"
        },
        {
            "key": "sig_figs",
            "label": "Significant figures shown",
            "format": "integer"
        }
    ],
    "formula": {
        "text": "x = a × 10ⁿ with 1 ≤ |a| < 10;  engineering notation uses an exponent that is a multiple of 3;  (a × 10ᵐ)(b × 10ⁿ) = ab × 10^(m+n)",
        "variables": {
            "a": "the coefficient (mantissa)",
            "n": "the power of ten"
        }
    },
    "worked_example": {
        "inputs": {
            "mode": "convert",
            "number": "0.000456",
            "a": "3e8",
            "op": "mul",
            "b": "2e-3",
            "sig": ""
        },
        "steps": [
            "Move the decimal point right until one non-zero digit is in front of it: 0.000456 → 4.56.",
            "It moved 4 places right, so the exponent is −4: 4.56 × 10⁻⁴.",
            "For engineering notation use the nearest lower multiple of 3: 456 × 10⁻⁶."
        ],
        "result": "0.000456 is 4.56 × 10⁻⁴ in scientific notation, 4.56e-4 in E notation and 456 × 10⁻⁶ in engineering notation."
    },
    "interpretation": "The exponent shows the order of magnitude and the coefficient’s digits are the significant figures. Engineering notation lines up with SI prefixes: 10³ kilo, 10⁻³ milli, 10⁻⁶ micro.",
    "assumptions": [
        "Calculations are exact on the decimal digits, except division, which is computed to at least 40 significant digits before rounding.",
        "Rounding to significant figures is half away from zero."
    ],
    "limitations": [
        "Exponents are limited to ±10,000."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Are trailing zeros significant?",
            "answer": "In 0.00045600 the trailing zeros after the decimal point count, giving 4.5600 × 10⁻⁴ (5 significant figures). In a whole number such as 123000 they are ambiguous, so they are not counted unless you set the significant figures."
        },
        {
            "question": "What does 6.02e23 mean?",
            "answer": "E notation is how calculators and programming languages write 6.02 × 10²³."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Rounding Calculator",
            "url": "https://calculators.geekmidst.com/calculators/rounding-calculator"
        },
        {
            "name": "Big Number Calculator",
            "url": "https://calculators.geekmidst.com/calculators/big-number-calculator"
        },
        {
            "name": "Percentage Calculator",
            "url": "https://calculators.geekmidst.com/calculators/percentage-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}