Scientific Notation Calculator
Convert numbers to and from scientific notation, E-notation, engineering notation, and decimal form
Check Scientific Notation Calculator
Notation Comparison
| Decimal | Scientific | E-notation | Engineering |
|---|---|---|---|
| 0.0000001 | 1 × 10⁻⁷ | 1e-7 | 100 × 10⁻⁹ |
| 0.001 | 1 × 10⁻³ | 1e-3 | 1 × 10⁻³ |
| 1 | 1 × 10⁰ | 1e0 | 1 × 10⁰ |
| 1,000 | 1 × 10³ | 1e3 | 1 × 10³ |
| 4,500,000 | 4.5 × 10⁶ | 4.5e6 | 4.5 × 10⁶ |
| 7,200,000,000 | 7.2 × 10⁹ | 7.2e9 | 7.2 × 10⁹ |
Common Scientific Constants
| Constant | Value | E-notation |
|---|---|---|
| Speed of light (c) | 2.998 × 10⁸ m/s | 2.998e8 |
| Avogadro's number (Nₐ) | 6.022 × 10²³ mol⁻¹ | 6.022e23 |
| Planck's constant (h) | 6.626 × 10⁻³⁴ J·s | 6.626e-34 |
| Electron mass (mₑ) | 9.109 × 10⁻³¹ kg | 9.109e-31 |
| Elementary charge (e) | 1.602 × 10⁻¹⁹ C | 1.602e-19 |
| Boltzmann constant (k) | 1.381 × 10⁻²³ J/K | 1.381e-23 |
Paste a decimal, E-notation value, or x10^ expression, then get normalized scientific notation, decimal form, engineering notation, and E-notation in one result panel.
How the result is built
Conversion Rule And Input Formats
Move the decimal point until one nonzero digit remains before it. The number of places moved becomes the exponent.
0.00072 moves the decimal 4 places right to become 7.2, so the scientific notation is 7.2 x 10^-4. In E-notation, that is 7.2e-4.
- Leaving the coefficient outside the 1 to 10 normalized range.
- Using a positive exponent for small numbers less than 1.
- Changing significant figures while converting notation.
- Confusing x10^ notation with E-notation accepted by code and spreadsheets.
- Decimal: 299792458 or 0.00000123
- E-notation: 6.022e23 or 1.6e-19
- x10^ form: 3.5x10^-12
Scientific Notation Rules, Formats, And Mistakes
Calculator Task Context
Use this calculator to convert very large or very small numbers into scientific notation and back to standard decimal form.
Formula And Method Used
The calculator moves the decimal point so one nonzero digit remains before it, then records the movement as a power of 10.
Worked Example
- For 45,600, move the decimal four places left to get 4.56.
- Therefore 45,600 = 4.56 x 10^4.
Common Mistakes And Limits
- The leading coefficient should be at least 1 and less than 10.
- Moving the decimal left gives a positive exponent; moving it right gives a negative exponent.
- Keep significant figures separate from mere placeholder zeros.
Related Calculators
Scientific notation vs E-notation
Scientific notation is the classroom and textbook form, such as 4.56 x 10^4. E-notation is the plain-text form, such as 4.56e4, used in spreadsheets, programming languages, calculator displays, and exported data files.
When engineering notation helps
Engineering notation keeps exponents as multiples of 3, which makes values easier to connect to metric prefixes. For example, 0.0000047 can be written as 4.7 x 10^-6, which aligns with micro-scale units.
Arithmetic with powers of ten
Multiplication and division combine exponents directly. Addition and subtraction require matching powers of ten before combining coefficients. Use the Exponent Calculator for focused exponent practice, or the Log Calculator when you need to solve for an unknown exponent.
References & Sources
Common result checks
Questions about this tool
- What counts as proper scientific notation?
- The coefficient should be at least 1 and less than 10 in magnitude, followed by a power of 10. For example, 45,600 becomes 4.56 x 10^4.
- What is E-notation?
- E-notation is the plain-text form used by calculators, spreadsheets, and code. For example, 6.022 x 10^23 is written as 6.022e23.
- How is engineering notation different?
- Engineering notation uses exponents that are multiples of 3, which lines up with metric prefixes such as kilo, mega, micro, and nano.
- Does scientific notation decide significant figures?
- No. Scientific notation shows magnitude compactly. Significant figures depend on the precision of the original measurement or rounding rule.