# Scientific notation calculator and standard form converter

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

Interactive version: https://www.calcopenly.com/math/scientific-notation-calculator
Subject: Math calculators

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.

## Inputs

- **Calculate** (options: 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** (options: +, −, ×, ÷)
- **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** (options: Round up (away from zero), Round to even (OpenStax Chemistry rule))

## Results

- Scientific notation — main result
- E notation
- Engineering notation
- Decimal notation
- With an SI prefix
- Significant figures
- Exponent n in a × 10ⁿ
- Unrounded result

## Formula

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

## Worked examples

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

- Calculate: Convert a number
- Number: 299792458
- **Scientific notation: 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**
- Checked against: 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
- **Scientific notation: 3.57096 × 10⁵**
- **E notation: 3.57096e5**
- **Significant figures: 6**
- Checked against: 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
- **Scientific notation: 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**
- Checked against: 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
- **Scientific notation: 5.7 × 10⁻⁴**
- **Engineering notation: 570 × 10⁻⁶**
- **With an SI prefix: 570 µ (micro)**
- **Significant figures: 2**
- Checked against: 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: no
- **Scientific notation: 1.26155 × 10⁵**
- **E notation: 1.26155e5**
- **Engineering notation: 126.155 × 10³**
- Checked against: 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
- **Scientific notation: 1.262 × 10⁵**
- **Decimal notation: 126,200**
- **Significant figures: 4**
- **Unrounded result: 126,155**
- Checked against: OpenStax Chemistry 2e §1.5 addition rule: 122500 (known to the hundreds) + 3655 = 126155, rounded to the hundreds = 126200

## Questions

### 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.

### How accurate is the scientific notation calculator and standard form converter?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 10 worked examples whose answers come from independent sources; for example, “Speed of light, 299,792,458 m/s (default)” is checked against SI defining constant c = 299 792 458 m/s (BIPM SI Brochure 9th ed.); notation forms by hand.

### Where does the method come from?

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).

## Sources

- [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)