# حاسبة الصيغة العلمية والتحويل إلى الصيغة القياسية

> Scientific notation calculator: convert between decimal, scientific, E and engineering notation, and add, subtract, multiply or divide with sig-fig rules.

النسخة التفاعلية: https://www.calcopenly.com/ar/math/scientific-notation-calculator
الموضوع: حاسبات الرياضيات

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.

## المدخلات

- **Calculate** (الخيارات: Convert a number, Two numbers)
- **Number**: Decimal (0.005600), E notation (5.6e-3) or scientific (5.6 × 10^-3). The default is the speed of light in m/s.
- **Round to significant figures**: Blank keeps the significant figures you typed.
- **First number**: Decimal, E notation or scientific, e.g. 1.2 × 10^5.
- **Operation** (الخيارات: +, −, ×, ÷)
- **Second number**
- **Apply significant-figure rules**: × and ÷ keep the fewest significant figures; + and − keep the least precise decimal place. Turn off for exact numbers and constants.
- **When the dropped part is exactly 5** (الخيارات: Round up (away from zero), Round to even (OpenStax Chemistry rule))

## النتائج

- الصيغة العلمية — النتيجة الرئيسية
- E notation
- Engineering notation
- Decimal notation
- With an SI prefix
- Significant figures
- Exponent n in a × 10ⁿ
- Unrounded result

## الصيغة

$$
x = a \times 10^{n},\ 1 \le |a| < 10 \qquad (a \times 10^{m})(b \times 10^{n}) = ab \times 10^{m+n}
$$

## أمثلة محلولة

### Speed of light, 299,792,458 m/s (default)

- Calculate: Convert a number
- Number: 299792458
- **الصيغة العلمية: 2.99792458 × 10⁸**
- **E notation: 2.99792458e8**
- **Engineering notation: 299.792458 × 10⁶**
- **Decimal notation: 299,792,458**
- **With an SI prefix: 299.792458 M (mega)**
- **Significant figures: 9**
- **Exponent n in a × 10ⁿ: 8**
- مصدر التحقق: ⁨SI defining constant c = 299 792 458 m/s (BIPM SI Brochure 9th ed.); notation forms by hand⁩

### 357,096 (Calculator Soup example)

- Calculate: Convert a number
- Number: 357096
- **الصيغة العلمية: 3.57096 × 10⁵**
- **E notation: 3.57096e5**
- **Significant figures: 6**
- مصدر التحقق: ⁨Calculator Soup scientific notation converter: 357,096 = 3.57096 × 10^5⁩

### 0.005600 keeps its trailing zeros (Calculator Soup example)

- Calculate: Convert a number
- Number: 0.005600
- **الصيغة العلمية: 5.600 × 10⁻³**
- **E notation: 5.600e-3**
- **Engineering notation: 5.600 × 10⁻³**
- **Decimal notation: 0.005600**
- **With an SI prefix: 5.600 m (milli)**
- **Significant figures: 4**
- **Exponent n in a × 10ⁿ: -3**
- مصدر التحقق: ⁨Calculator Soup scientific notation converter: 0.005600 = 5.600 × 10^-3, trailing zeros kept as significant⁩

### 0.00057 in engineering notation (Omni Calculator example)

- Calculate: Convert a number
- Number: 0.00057
- **الصيغة العلمية: 5.7 × 10⁻⁴**
- **Engineering notation: 570 × 10⁻⁶**
- **With an SI prefix: 570 µ (micro)**
- **Significant figures: 2**
- مصدر التحقق: ⁨Omni Calculator scientific notation page: 0.00057 = 5.7 × 10⁻⁴; engineering form by moving to the next lower multiple of 3⁩

### 122,500 + 3,655 without sig-fig rules (Calculator Soup example)

- Calculate: Two numbers
- First number: 122500
- Operation: +
- Second number: 3655
- Apply significant-figure rules: لا
- **الصيغة العلمية: 1.26155 × 10⁵**
- **E notation: 1.26155e5**
- **Engineering notation: 126.155 × 10³**
- مصدر التحقق: ⁨Calculator Soup scientific notation calculator example: 122500 + 3655 = 1.26155 × 10^5⁩

### 122,500 + 3,655 with sig-fig rules

- Calculate: Two numbers
- First number: 122500
- Operation: +
- Second number: 3655
- **الصيغة العلمية: 1.262 × 10⁵**
- **Decimal notation: 126,200**
- **Significant figures: 4**
- **Unrounded result: 126,155**
- مصدر التحقق: ⁨OpenStax Chemistry 2e §1.5 addition rule: 122500 (known to the hundreds) + 3655 = 126155, rounded to the hundreds = 126200⁩

## الأسئلة

### How do you convert a number to scientific notation?

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.

### How do you multiply and divide numbers in scientific notation?

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.

### How do you add or subtract in scientific notation?

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.

### What is E notation, as in 6.02E23?

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.

### What is the difference between scientific and engineering notation?

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.

### ما مدى دقة «⁨حاسبة الصيغة العلمية والتحويل إلى الصيغة القياسية⁩»؟

تعتمد الدقة على مدخلاتك وافتراضات الطريقة. يستخدم الحساب العشري 50 رقمًا معنويًا، لكن التقديرات والأساليب العددية وبيانات المصدر قد تكون أقل دقة؛ تقريب القيم المعروضة لا يزيل هذه الحدود. أمثلة محلولة جرى التحقق منها بمصادر مستقلة: 10. مثلًا، يجري التحقق من «⁨Speed of light, 299,792,458 m/s (default)⁩» بالرجوع إلى ⁨SI defining constant c = 299 792 458 m/s (BIPM SI Brochure 9th ed.); notation forms by hand⁩.

### ما مصدر هذه الطريقة؟

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).

## المصادر

- [OpenStax, Chemistry 2e, §1.5 Measurement uncertainty, accuracy, and precision (significant-figure rules)](https://openstax.org/books/chemistry-2e/pages/1-5-measurement-uncertainty-accuracy-and-precision)
- [BIPM, SI prefixes (SI Brochure, 9th edition, and CGPM 2022 Resolution 3)](https://www.bipm.org/en/measurement-units/si-prefixes)
- [NIST SP 811, Guide for the Use of the International System of Units (SI), chapters 7 and 10 (expressing values and printing numbers)](https://www.nist.gov/pml/special-publication-811)