{
  "id": "fraction-to-percentage",
  "version": "f9b557e5ba51",
  "status": "published",
  "name": "Fraction to Percent Calculator",
  "question": "How to change fraction to percent?",
  "summary": "Turns a fraction or mixed number into a percent: the exact percent when its decimal ends (5/8 is 62.5%), or rounded to the places you pick (1/3 is about 33.33%).",
  "category": "math",
  "subcategory": "percentages",
  "url": "https://www.acalculator.org/math/fraction-to-percentage",
  "markdown": "https://www.acalculator.org/math/fraction-to-percentage.md",
  "kind": "function",
  "method": "percent = numerator ÷ denominator × 100. The decimal ends when the denominator in lowest terms has no prime factor other than 2 and 5; then the percent is exact. Otherwise it is rounded, halves away from zero.",
  "assumptions": [
    "The fraction is reduced to lowest terms first; all arithmetic is exact.",
    "A rounded percent keeps exactly the chosen number of decimal places; halves round away from zero."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "f": {
        "title": "Fraction",
        "description": "A fraction, mixed number, or whole number, such as 5/8, 1 3/4, or 2/3.",
        "type": "string",
        "pattern": "^-?\\d+( \\d+)?(/\\d+)?$"
      },
      "dp": {
        "title": "Round to (decimal places)",
        "description": "How many decimal places the rounded percent keeps, from 0 to 10.",
        "type": "integer",
        "minimum": 0,
        "maximum": 10
      }
    }
  },
  "outputs": {
    "percent": {
      "label": "Percent",
      "description": "The exact percent when its decimal ends; otherwise the rounded percent after ≈.",
      "format": "text"
    },
    "rounded": {
      "label": "Rounded percent",
      "description": "The percent rounded to the chosen decimal places; halves round away from zero.",
      "format": "text"
    },
    "decimal": {
      "label": "Decimal",
      "description": "The fraction as a decimal: exact when it ends, else rounded to 2 more places than the percent.",
      "format": "text"
    },
    "exact": {
      "label": "Exact?",
      "description": "Yes when the decimal ends, so the percent is exact; no when it repeats.",
      "format": "text"
    },
    "work": {
      "label": "How",
      "description": "The fraction divided out, then times 100.",
      "format": "text"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "f": "5/8",
      "dp": 2
    },
    "outputs": {
      "percent": "62.5%",
      "rounded": "62.50%",
      "decimal": "0.625",
      "exact": "yes",
      "work": "5/8 = 5 ÷ 8 = 0.625; 0.625 × 100 = 62.5%"
    },
    "text": "5/8 = 5 ÷ 8 = 0.625; 0.625 × 100 = 62.5%."
  },
  "examples": [
    {
      "given": {
        "f": "5/8",
        "dp": 2
      },
      "expect": {
        "percent": "62.5%",
        "rounded": "62.50%",
        "decimal": "0.625",
        "exact": "yes",
        "work": "5/8 = 5 ÷ 8 = 0.625; 0.625 × 100 = 62.5%"
      },
      "source": "OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05); hand calculation in content.mdx"
    },
    {
      "given": {
        "f": "1/3",
        "dp": 2
      },
      "expect": {
        "percent": "≈ 33.33%",
        "decimal": "0.3333",
        "exact": "no, the decimal repeats"
      },
      "source": "OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05); hand calculation in content.mdx: 1 ÷ 3 = 0.333…"
    },
    {
      "given": {
        "f": "2/3",
        "dp": 1
      },
      "expect": {
        "percent": "≈ 66.7%",
        "rounded": "66.7%"
      },
      "source": "OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05); hand calculation in content.mdx: 66.666… rounds up to 66.7"
    },
    {
      "given": {
        "f": "1 3/4",
        "dp": 0
      },
      "expect": {
        "percent": "175%",
        "rounded": "175%",
        "decimal": "1.75"
      },
      "source": "OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05); hand calculation in content.mdx: 1 3/4 = 7/4 = 1.75"
    },
    {
      "given": {
        "f": "-1/8",
        "dp": 1
      },
      "expect": {
        "percent": "−12.5%",
        "rounded": "−12.5%",
        "decimal": "−0.125"
      },
      "source": "OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05); hand calculation in content.mdx: 1 ÷ 8 = 0.125, with the minus sign"
    },
    {
      "given": {
        "f": "1/16",
        "dp": 0
      },
      "expect": {
        "percent": "6.25%",
        "rounded": "6%"
      },
      "source": "OpenStax, Prealgebra 2e, §6.1 Understand Percent (convert a fraction to a percent: write it as a decimal, then multiply by 100), https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent (retrieved 2026-10-05); hand calculation in content.mdx: 1 ÷ 16 = 0.0625"
    }
  ],
  "sources": [
    "OpenStax, Prealgebra 2e, §6.1 Understand Percent: to convert a fraction to a percent, convert the fraction to a decimal, then convert the decimal to a percent (multiply by 100). CC BY 4.0. Retrieved 2026-10-05. https://openstax.org/books/prealgebra-2e/pages/6-1-understand-percent",
    "OpenStax, Prealgebra 2e, §5.3 Decimals and Fractions: a fraction as a decimal by dividing; repeating decimals. CC BY 4.0. Retrieved 2026-10-05. https://openstax.org/books/prealgebra-2e/pages/5-3-decimals-and-fractions"
  ],
  "related": [
    "fraction-to-decimal",
    "decimal-to-percentage",
    "percentage",
    "simplify-fraction"
  ],
  "changelog": []
}