{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"scientific-notation"},"result":{"entity_type":"calculator","id":"scientific-notation","calculator_id":"scientific-notation","canonical_url":"https://tttkmbb.com/math/scientific-notation","name":"Scientific Notation Converter","title":"Scientific Notation Converter – Mantissa, Exponent, E-Notation and Engineering Notation","category":"math","category_name":"Math","tool_name":"convert_to_scientific_notation","featured_mcp_tool":false,"description":"Writes a number in normalised scientific notation m × 10^e with 1 ≤ |m| < 10, in E-notation, and in engineering notation (exponent a multiple of 3).","use_when":"You need a very large or very small number in scientific or engineering form, or its order of magnitude.","do_not_use_when":"You want to round a number to a given precision (use rounding) or compute a power (use exponent).","inputs":[{"name":"value","label":"Value","type":"number","required":true,"min":-1e+300,"max":1e+300,"description":"Any number, e.g. 123400 or 0.000123.","example":123400}],"outputs":[{"name":"mantissa","label":"Mantissa (m)","type":"number","decimals":10,"description":"Significand with 1 ≤ |m| < 10 (0 for zero)."},{"name":"exponent","label":"Exponent (e)","type":"integer","decimals":0,"description":"Power of 10 such that value = m × 10^e; also the order of magnitude."},{"name":"scientific_notation","label":"Scientific notation","type":"string","decimals":4,"description":"e.g. '1.234 × 10^5'."},{"name":"e_notation","label":"E notation","type":"string","decimals":4,"description":"Calculator/programming form, e.g. '1.234e5'."},{"name":"engineering_notation","label":"Engineering notation","type":"string","decimals":4,"description":"Exponent a multiple of 3 and mantissa between 1 and 999.999…, e.g. '123.4 × 10^3'."},{"name":"engineering_mantissa","label":"Engineering mantissa","type":"number","decimals":10,"description":"Mantissa of the engineering form."},{"name":"engineering_exponent","label":"Engineering exponent","type":"integer","decimals":0,"description":"Exponent of the engineering form (…, −6, −3, 0, 3, 6, …)."}],"input_schema":{"type":"object","properties":{"value":{"description":"Any number, e.g. 123400 or 0.000123.","type":"number","minimum":-1e+300,"maximum":1e+300,"examples":[123400]}},"additionalProperties":false,"required":["value"]},"output_schema":{"type":"object","properties":{"mantissa":{"description":"Significand with 1 ≤ |m| < 10 (0 for zero).","type":"number"},"exponent":{"description":"Power of 10 such that value = m × 10^e; also the order of magnitude.","type":"integer"},"scientific_notation":{"description":"e.g. '1.234 × 10^5'.","type":"string"},"e_notation":{"description":"Calculator/programming form, e.g. '1.234e5'.","type":"string"},"engineering_notation":{"description":"Exponent a multiple of 3 and mantissa between 1 and 999.999…, e.g. '123.4 × 10^3'.","type":"string"},"engineering_mantissa":{"description":"Mantissa of the engineering form.","type":"number"},"engineering_exponent":{"description":"Exponent of the engineering form (…, −6, −3, 0, 3, 6, …).","type":"integer"}}},"formula":"e = ⌊log10|value|⌋, m = value / 10^e; engineering: e₃ = 3·⌊e/3⌋, m₃ = value / 10^e₃","method":"The digits come from the shortest decimal representation that round-trips the input, so 0.000123 is reported as 1.23 × 10^-4 without floating-point noise.","sources":[{"name":"Wikipedia – Scientific notation","url":"https://en.wikipedia.org/wiki/Scientific_notation","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wikipedia – Engineering notation","url":"https://en.wikipedia.org/wiki/Engineering_notation","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wolfram MathWorld – Scientific Notation","url":"https://mathworld.wolfram.com/ScientificNotation.html","type":"reference","retrieved_at":"2026-09-23"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"123400","inputs":{"value":123400},"expected":{"mantissa":1.234,"exponent":5,"scientific_notation":"1.234 × 10^5","e_notation":"1.234e5","engineering_notation":"123.4 × 10^3","engineering_mantissa":123.4,"engineering_exponent":3},"url":"https://tttkmbb.com/api/v1/calculate/scientific-notation?value=123400"},{"name":"0.000123","inputs":{"value":0.000123},"expected":{"mantissa":1.23,"exponent":-4,"scientific_notation":"1.23 × 10^-4","e_notation":"1.23e-4","engineering_notation":"123 × 10^-6","engineering_mantissa":123,"engineering_exponent":-6},"url":"https://tttkmbb.com/api/v1/calculate/scientific-notation?value=0.000123"}],"faq":[{"q":"What is the difference between scientific and engineering notation?","a":"Scientific notation keeps one digit before the decimal point; engineering notation uses exponents that are multiples of 3 so the number maps onto SI prefixes (10^3 = kilo, 10^-6 = micro)."},{"q":"How many digits are kept?","a":"All significant digits of the input (up to 12 in the text forms); to shorten the mantissa, round the value first with the rounding calculator."}],"tags":["scientific notation","standard form","engineering notation","e notation","order of magnitude","mantissa exponent"],"related":[{"calculator_id":"rounding","reason":"Round to a number of significant figures before formatting."},{"calculator_id":"exponent","reason":"Evaluate powers of 10 and other bases."},{"calculator_id":"logarithm","reason":"log10 gives the exponent directly."}],"links":{"html":"https://tttkmbb.com/math/scientific-notation","markdown":"https://tttkmbb.com/math/scientific-notation.md","json":"https://tttkmbb.com/math/scientific-notation.json","api":"https://tttkmbb.com/api/v1/calculate/scientific-notation","schema":"https://tttkmbb.com/api/v1/calculators/scientific-notation","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:22:59Z"}