Scientific notation calculator: convert between decimal, scientific, E and engineering notation, and add, subtract, multiply or divide with sig-fig rules.
업데이트 검증한 예제: 10
299792458 is 2.99792458 × 10⁸ in scientific notation, 2.99792458e8 in E notation and 299.792458 × 10⁶ in engineering notation, with 9 significant figures.
299792458 has 9 significant figures.
The point moves 8 places left to sit after the first significant digit, so the exponent is 8.
Engineering notation lowers the exponent to a multiple of 3 (6); E notation writes “× 10^” as e: 2.99792458e8.
Scientific notation writes a number as a × 10ⁿ with 1 ≤ |a| < 10, so 299,792,458 becomes 2.99792458 × 10⁸: the decimal point moves 8 places left and the exponent counts the moves. E notation writes the same number as 2.99792458e8, and engineering notation keeps the exponent a multiple of 3 (299.792458 × 10⁶) so it lines up with SI prefixes such as mega. In the UK this form is called standard form.
The digits you type set the significant figures, and they are kept: 0.005600 converts to 5.600 × 10⁻³ with four. For arithmetic, products and quotients keep the fewest significant figures of the inputs, and sums and differences keep the least precise decimal place, the rules in OpenStax Chemistry 2e §1.5. For example, 1.2 × 10⁵ × 3.45 × 10⁻² = 4,140 is reported as 4.1 × 10³.
Trailing zeros in a whole number without a decimal point, as in 93,000,000, are treated as placeholders; type 93,000,000. or 9.300 × 10^7 when they were measured.
검증 출처: SI defining constant c = 299 792 458 m/s (BIPM SI Brochure 9th ed.); notation forms by hand
검증 출처: Calculator Soup scientific notation converter: 357,096 = 3.57096 × 10^5
검증 출처: Calculator Soup scientific notation converter: 0.005600 = 5.600 × 10^-3, trailing zeros kept as significant
검증 출처: Omni Calculator scientific notation page: 0.00057 = 5.7 × 10⁻⁴; engineering form by moving to the next lower multiple of 3
Move the decimal point until one non-zero digit is left of it, and count the moves. Moving left gives a positive exponent and moving right a negative one. 357,096 needs 5 moves left, so it is 3.57096 × 10⁵; 0.005600 needs 3 moves right, so it is 5.600 × 10⁻³. Keep every significant digit, including the trailing zeros after a decimal point.
Multiply or divide the leading numbers and add or subtract the exponents, then renormalize. (1.2 × 10⁵) × (3.45 × 10⁻²) = 4.14 × 10³, and (6.0 × 10⁴) ÷ (1.5 × 10⁻²) = 4.0 × 10⁶. With measured values, round the answer to the fewest significant figures among the inputs: 1.2 has two, so the product is 4.1 × 10³.
Rewrite both numbers with the same power of ten, add or subtract the leading numbers, then renormalize. 1.225 × 10⁵ + 3.655 × 10³ = 1.225 × 10⁵ + 0.03655 × 10⁵ = 1.26155 × 10⁵. For measurements, round to the least precise decimal place: 122,500 is known to the hundreds, so the sum is 126,200, or 1.262 × 10⁵.
E notation is scientific notation for calculators, spreadsheets and programming languages, where E (or e) stands for “times ten to the power”. 6.02E23 means 6.02 × 10²³, and 5.6e-3 means 5.6 × 10⁻³ = 0.0056. Excel shows numbers of 12 or more digits this way in the General format, and most languages accept it in number literals.
Engineering notation restricts the exponent to multiples of 3, so the leading number is between 1 and 1,000. 0.00057 is 5.7 × 10⁻⁴ in scientific notation but 570 × 10⁻⁶ in engineering notation, which reads directly as 570 micro-units. The multiples of 3 match the SI prefixes from quecto (10⁻³⁰) to quetta (10³⁰), the range set by the 2022 General Conference on Weights and Measures.
정확도는 입력값과 계산 방법의 가정에 따라 달라집니다. 십진 연산은 유효숫자 50자리를 사용하지만, 추정값·수치해석 방법·원본 데이터의 정밀도는 더 낮을 수 있습니다. 표시값을 반올림해도 이러한 한계는 사라지지 않습니다. 독립적인 출처의 풀이와 대조한 계산 예시: 10. 예를 들어 “Speed of light, 299,792,458 m/s (default)”은 SI defining constant c = 299 792 458 m/s (BIPM SI Brochure 9th ed.); notation forms by hand와 대조해 확인합니다.
OpenStax, Chemistry 2e, §1.5 Measurement uncertainty, accuracy, and precision (significant-figure rules); BIPM, SI prefixes (SI Brochure, 9th edition, and CGPM 2022 Resolution 3); NIST SP 811, Guide for the Use of the International System of Units (SI), chapters 7 and 10 (expressing values and printing numbers).
이 계산기에는 독립적인 출처에서 답을 얻은 계산 예제가 10개 있습니다. 테스트 모음에서 실행되며 여기에서도 실행할 수 있습니다.
소수 자릿수, 유효 숫자 또는 가장 가까운 10이나 100의 배수로 수를 반올림합니다. 중간값을 짝수로 반올림하기, 음의 무한대 방향 또는 양의 무한대 방향으로 반올림하기 등 아홉 가지 규칙을 제공합니다.
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Y의 X%, 한 수가 다른 수에서 차지하는 백분율, 백분율 증가 또는 감소, 백분율 차이, 그리고 일정 비율을 더하기 전의 원래 값을 구합니다.