Scientific Notation Converter
Convert any number between standard decimal form, scientific notation, E-notation and engineering notation with SI prefixes, and multiply, divide, add or subtract numbers in scientific notation with steps. Exact digit-by-digit math runs in your browser.
Examples: 299792458 · 0.00004567 · 6.022 × 10^23 · 1.6e-19 · 4.5x10⁻³ · 12,500,000
How to use the Scientific Notation Converter
- Type or paste a number in any form, for example 0.00004567, 12,500,000 or 6.022 × 10^23.
- Read the results: scientific notation, standard form, E-notation, engineering notation, the SI prefix and LaTeX update instantly.
- Choose significant figures if you want the result rounded, or leave Auto to keep the digits you typed.
- Press Copy next to any format to copy it.
- Calculate: on the Calculate tab enter two numbers, pick ×, ÷, + or − and press Calculate to see the answer in scientific notation with steps.
Scientific notation examples
| Standard form | Scientific notation | E-notation | Engineering / SI |
|---|---|---|---|
| 299,792,458 (speed of light, m/s) | 2.99792458 × 10⁸ | 2.99792458e8 | 299.792458 × 10⁶ (M) |
| 602,214,076,000,000,000,000,000 | 6.02214076 × 10²³ | 6.02214076e23 | 602.214076 × 10²¹ (Z) |
| 45,600 | 4.56 × 10⁴ | 4.56e4 | 45.6 × 10³ (k) |
| 0.0071 | 7.1 × 10⁻³ | 7.1e-3 | 7.1 × 10⁻³ (m) |
| 0.00004567 | 4.567 × 10⁻⁵ | 4.567e-5 | 45.67 × 10⁻⁶ (µ) |
| 0.000000000000000000160217663 | 1.60217663 × 10⁻¹⁹ | 1.60217663e-19 | 160.217663 × 10⁻²¹ (z) |
SI prefixes and powers of ten
| Prefix | Symbol | Power | Prefix | Symbol | Power |
|---|---|---|---|---|---|
| kilo | k | 10³ | milli | m | 10⁻³ |
| mega | M | 10⁶ | micro | µ | 10⁻⁶ |
| giga | G | 10⁹ | nano | n | 10⁻⁹ |
| tera | T | 10¹² | pico | p | 10⁻¹² |
| peta | P | 10¹⁵ | femto | f | 10⁻¹⁵ |
| exa | E | 10¹⁸ | atto | a | 10⁻¹⁸ |
| zetta | Z | 10²¹ | zepto | z | 10⁻²¹ |
| yotta | Y | 10²⁴ | yocto | y | 10⁻²⁴ |
| ronna | R | 10²⁷ | ronto | r | 10⁻²⁷ |
| quetta | Q | 10³⁰ | quecto | q | 10⁻³⁰ |
Ronna, ronto, quetta and quecto were added to the SI in 2022 by the General Conference on Weights and Measures (CGPM).
Rules for calculating in scientific notation
- Multiply: multiply the coefficients, add the exponents. (2 × 10³) × (4 × 10⁵) = 8 × 10⁸.
- Divide: divide the coefficients, subtract the exponents. (6 × 10⁸) ÷ (3 × 10²) = 2 × 10⁶.
- Add or subtract: rewrite both numbers with the same exponent first. 5.2 × 10⁴ + 3.1 × 10³ = 5.2 × 10⁴ + 0.31 × 10⁴ = 5.51 × 10⁴.
- Normalize: if the coefficient ends up 10 or larger, or smaller than 1, move the decimal point and adjust the exponent: 12.8 × 10² = 1.28 × 10³.
- Powers: raise the coefficient and multiply the exponent: (3 × 10⁴)² = 9 × 10⁸. The exponent calculator handles any power.
To check how many significant figures an answer should keep, use the scientific calculator together with the significant figure rules: the fewest significant figures for × and ÷, the least precise decimal place for + and −.
Frequently asked questions
How do you convert a number to scientific notation?
Move the decimal point until exactly one non-zero digit is left of it; the number of places moved is the exponent. Moving left gives a positive exponent and moving right a negative one. 45,600 becomes 4.56 × 10⁴ and 0.00045 becomes 4.5 × 10⁻⁴.
How do you convert scientific notation to standard form?
Move the decimal point by the exponent: to the right for a positive exponent and to the left for a negative one, filling gaps with zeros. 3.2 × 10⁵ = 320,000 and 7.1 × 10⁻³ = 0.0071.
What is E-notation?
E-notation is how calculators and programming languages write scientific notation: the E (or e) means 'times ten to the power of'. 6.022E23 means 6.022 × 10²³ and 1.6e-19 means 1.6 × 10⁻¹⁹. Spreadsheets show it as 6.02E+23.
What is the difference between scientific and engineering notation?
In scientific notation the coefficient is between 1 and 10. In engineering notation the exponent is always a multiple of 3, so the coefficient is between 1 and 1000. 45,600 is 4.56 × 10⁴ in scientific notation and 45.6 × 10³ in engineering notation, which matches the SI prefix: 45.6 k.
What does 'standard form' mean?
In the US, standard form usually means an ordinary decimal number such as 320,000. In the UK and many other countries, 'standard form' means scientific notation (3.2 × 10⁵). This converter shows both.
How do you multiply and divide numbers in scientific notation?
Multiply (or divide) the coefficients and add (or subtract) the exponents, then normalize. (3.2 × 10⁵) × (4.0 × 10⁻³) = 12.8 × 10² = 1.28 × 10³. To add or subtract, first rewrite both numbers with the same power of ten.
How many significant figures does the converter keep?
By default it keeps every digit you typed, except trailing zeros in a whole number without a decimal point (1,200 gives 1.2 × 10³), which are ambiguous. Choose a number of significant figures to round or to keep those zeros.