{
  "id": "standard-form",
  "version": "89bd5afe6e25",
  "status": "published",
  "name": "Standard Form Calculator",
  "question": "What is it in standard form?",
  "summary": "Writes a number in standard form a × 10ⁿ, in standard notation with all its digits, and in expanded form, from a decimal, E notation, a × 10ⁿ, or a sum such as 100 + 30 + 8.",
  "category": "math",
  "subcategory": "arithmetic",
  "url": "https://www.acalculator.org/math/standard-form-calculator",
  "markdown": "https://www.acalculator.org/math/standard-form-calculator.md",
  "kind": "function",
  "method": "Standard form: a × 10ⁿ with 1 ≤ |a| < 10, where n counts the places the decimal point moves (left is positive). Expanded form: each non-zero digit times its place value.",
  "assumptions": [
    "In the UK, standard form means a × 10ⁿ; in US schools, standard form means the number written with digits, which this page calls standard notation.",
    "Digits are exact as typed: nothing is rounded through binary floating point.",
    "Leading zeros are never significant; trailing zeros of a whole number without a decimal point are not kept in a.",
    "Rounding to significant figures rounds an exact half to the even digit (2.45 → 2.4)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "n": {
        "title": "Number",
        "description": "The number: a decimal such as 154.37 or 0.00045, E notation such as 4.5e-4, a × 10ⁿ such as 4.5 × 10^-4, or a sum such as 100 + 50 + 4.",
        "type": "string",
        "maxLength": 200
      },
      "sf": {
        "title": "Round to significant figures",
        "description": "Optional: how many significant figures to keep, from 1 to 30. Leave empty to keep them all.",
        "type": "integer",
        "minimum": 1,
        "maximum": 30
      }
    }
  },
  "outputs": {
    "standard": {
      "label": "Standard form (a × 10ⁿ)",
      "description": "The number as a × 10ⁿ with one non-zero digit before the point of a: standard form in the UK, scientific notation in the US.",
      "format": "text"
    },
    "decimal": {
      "label": "Standard notation",
      "description": "The number with all its digits written out, as in US school standard form, for powers from 10⁻³⁰ to 10³⁰.",
      "format": "text"
    },
    "expanded": {
      "label": "Expanded form",
      "description": "Each non-zero digit times its place value, added up.",
      "format": "text"
    },
    "powers": {
      "label": "Expanded form with powers of ten",
      "description": "Each non-zero digit times its power of ten, added up.",
      "format": "text"
    },
    "e": {
      "label": "E notation",
      "description": "The standard form as calculators and spreadsheets write it: a e n means a × 10ⁿ.",
      "format": "text"
    },
    "exponent": {
      "label": "Exponent n",
      "description": "The power of ten in a × 10ⁿ.",
      "format": "integer"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "n": "154.37"
    },
    "outputs": {
      "standard": "1.5437 × 10²",
      "decimal": "154.37",
      "expanded": "100 + 50 + 4 + 0.3 + 0.07",
      "powers": "1 × 10² + 5 × 10¹ + 4 × 10⁰ + 3 × 10⁻¹ + 7 × 10⁻²",
      "e": "1.5437e2",
      "exponent": 2
    },
    "text": "154.37 in standard form is 1.5437 × 10²."
  },
  "examples": [
    {
      "given": {
        "n": "154.37"
      },
      "expect": {
        "standard": "1.5437 × 10²",
        "decimal": "154.37",
        "expanded": "100 + 50 + 4 + 0.3 + 0.07",
        "powers": "1 × 10² + 5 × 10¹ + 4 × 10⁰ + 3 × 10⁻¹ + 7 × 10⁻²",
        "exponent": 2
      },
      "source": "OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶), https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation, retrieved 2026-10-02; OpenStax, Prealgebra 2e, section 1.1 Introduction to Whole Numbers (standard form 138 and expanded form 100 + 30 + 8), https://openstax.org/books/prealgebra-2e/pages/1-1-introduction-to-whole-numbers, retrieved 2026-10-02; hand calculation in content.mdx"
    },
    {
      "given": {
        "n": "2,780,418"
      },
      "expect": {
        "standard": "2.780418 × 10⁶",
        "e": "2.780418e6",
        "expanded": "2,000,000 + 700,000 + 80,000 + 400 + 10 + 8"
      },
      "source": "OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶), https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation, retrieved 2026-10-02, example: 2,780,418 = 2.780418 × 10⁶"
    },
    {
      "given": {
        "n": "0.00000000000047"
      },
      "expect": {
        "standard": "4.7 × 10⁻¹³",
        "decimal": "0.00000000000047",
        "expanded": "0.0000000000004 + 0.00000000000007"
      },
      "source": "OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶), https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation, retrieved 2026-10-02, example: 0.00000000000047 = 4.7 × 10⁻¹³"
    },
    {
      "given": {
        "n": "100 + 30 + 8"
      },
      "expect": {
        "decimal": "138",
        "standard": "1.38 × 10²",
        "powers": "1 × 10² + 3 × 10¹ + 8 × 10⁰"
      },
      "source": "OpenStax, Prealgebra 2e, section 1.1 Introduction to Whole Numbers (standard form 138 and expanded form 100 + 30 + 8), https://openstax.org/books/prealgebra-2e/pages/1-1-introduction-to-whole-numbers, retrieved 2026-10-02, example: 100 + 30 + 8 is 138 in standard form"
    },
    {
      "given": {
        "n": "4.5 × 10^-4"
      },
      "expect": {
        "decimal": "0.00045",
        "standard": "4.5 × 10⁻⁴",
        "expanded": "0.0004 + 0.00005"
      },
      "source": "OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶), https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation, retrieved 2026-10-02; hand calculation in content.mdx: move the point 4 places left"
    },
    {
      "given": {
        "n": "154.37",
        "sf": 3
      },
      "expect": {
        "standard": "1.54 × 10²",
        "decimal": "154",
        "expanded": "100 + 50 + 4",
        "e": "1.54e2"
      },
      "source": "OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶), https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation, retrieved 2026-10-02; hand calculation in content.mdx: 1.54|37 drops less than half, so 1.54"
    },
    {
      "given": {
        "n": "-3050"
      },
      "expect": {
        "standard": "−3.05 × 10³",
        "decimal": "−3,050",
        "expanded": "−(3,000 + 50)"
      },
      "source": "hand calculation in content.mdx: −3,050 = −(3,000 + 50) = −3.05 × 10³"
    }
  ],
  "sources": [
    "OpenStax, Algebra and Trigonometry 2e, section 1.2 Exponents and Scientific Notation (a × 10ⁿ with 1 ≤ |a| < 10; 2,780,418 = 2.780418 × 10⁶; 0.00000000000047 = 4.7 × 10⁻¹³), CC BY 4.0, retrieved 2026-10-02. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-2-exponents-and-scientific-notation",
    "OpenStax, Prealgebra 2e, section 1.1 Introduction to Whole Numbers (standard form 138; expanded form 100 + 30 + 8), CC BY 4.0, retrieved 2026-10-02. https://openstax.org/books/prealgebra-2e/pages/1-1-introduction-to-whole-numbers"
  ],
  "related": [
    "scientific-notation",
    "rounding",
    "exponent"
  ],
  "changelog": []
}