Scientific Notation Converter
Convert a plain number such as 320000 into scientific notation (3.20 × 105), E-notation (3.20e5) and engineering notation, choosing how many significant figures to keep. Or enter 3.2e5 or 3.2 × 105 and get the decimal back. Each conversion shows the decimal-point move behind it. Free, no sign-up.
What are you entering?
How to Use the Scientific Notation Converter
- 1. Choose what you are entering. Decimal number → scientific starts from a plain number. The other two options start from scientific notation (3.2 × 105) or E-notation (3.2e5) and give the decimal.
- 2. Type the number. For notation input, 3.2e5, 3.2E-4, 3.2 x 10^5 and 3.2 × 105 are all accepted.
- 3. Set significant figures. In decimal mode, pick 2 to 10 significant figures (3 is the default). The coefficient is rounded to that many digits.
- 4. Read the results and steps. You get the three forms of the answer, then the working: how far the decimal point moved and which way.
The Three Notations
| Form | Rule | Example (320000) |
|---|---|---|
| Scientific | a × 10n, with 1 ≤ |a| < 10 and n an integer | 3.20 × 105 |
| E-notation | The same, with "× 10^" replaced by e or E, as in calculators and code | 3.20e5 |
| Engineering | Like scientific, but n is a multiple of 3, so 1 ≤ |a| < 1000 | 320 × 103 |
Scientific notation is called standard form in the UK and parts of the Commonwealth. Engineering notation lines up with SI prefixes — 103 is kilo, 106 mega, 10−3 milli — so 320 × 103 reads directly as 320 kilo-units.
How to Convert by Hand
Move the decimal point until exactly one nonzero digit is to its left, and count the places. Moving it left makes the exponent positive; moving it right makes it negative. To go back, move the point the number of places the exponent says — right for a positive exponent, left for a negative one — padding with zeros.
| Decimal | Significant figures | Scientific | Engineering |
|---|---|---|---|
| 320000 | 3 | 3.20 × 105 | 320 × 103 |
| 0.00047 | 3 | 4.70 × 10−4 | 470 × 10−6 |
| 299792458 | 3 | 3.00 × 108 | 300 × 106 |
| 299792458 | 6 | 2.99792 × 108 | 299.792 × 106 |
| 12500 | 3 | 1.25 × 104 | 12.5 × 103 |
| −45000 | 3 | −4.50 × 104 | −45 × 103 |
Notice that the significant-figures setting rounds: the speed of light, 299792458 m/s, becomes 3.00 × 108 at three figures. The trailing zeros in 3.20 and 3.00 are kept in the scientific form because they are significant; the engineering form drops them. If you are rounding to a stated number of significant figures, check your count with the Significant Figures Calculator.
Limits of the Tool
- Doubles, not exact decimals. Decimal input is read as a standard floating-point number, so it carries about 15 to 17 significant digits. Beyond that the extra digits are not reliable.
- Exponents up to ±1000. Larger exponents in notation input are refused.
- Notation input is rewritten to standard form. In the two notation modes the normalized and E-notation rows move the point so one nonzero digit sits before it: 45e3 becomes 4.5 × 104 and 0.0045e3 becomes 4.5 × 100. Digits you type after a decimal point are kept, so 3.20e5 stays 3.20 × 105; the steps still show your original coefficient.
- Zero is special. It is shown as 0 × 100.
Which Tool Do You Need?
| You want to… | Use |
|---|---|
| Convert a number to or from scientific, E or engineering notation | This converter |
| Count or round to a number of significant figures | Significant Figures Calculator |
| Convert between kilo, mega, milli, micro and other prefixes | Metric Prefix Converter |
| Convert metric and imperial units | Unit Converter |
| Show a number in binary, octal or hex | Number Base Converter |
Frequently Asked Questions
- What is scientific notation?
- It writes a number as a × 10n, where the coefficient a is at least 1 and less than 10 and the exponent n is an integer. So 320,000 is 3.2 × 105 and 0.00047 is 4.7 × 10−4. It keeps very large and very small numbers short and makes the significant figures obvious.
- What is E-notation?
- E-notation is the calculator and programming form of scientific notation, with the "× 10^" replaced by the letter e. 3.2 × 105 is written 3.2e5 and 4.7 × 10−4 is written 4.7e-4. The e stands for exponent, not for Euler's number.
- What is engineering notation?
- Engineering notation is scientific notation with the exponent restricted to multiples of 3, so the coefficient runs from 1 up to just under 1000. It matches SI prefixes: 320 × 103 is 320 kilo-units and 470 × 10−6 is 470 micro-units.
- How do I convert a number to scientific notation by hand?
- Move the decimal point until one nonzero digit is left of it and count the places moved. Left gives a positive exponent, right a negative one. For 5,600, move 3 places left to get 5.6 × 103; for 0.0042, move 3 places right to get 4.2 × 10−3.
- What does the significant figures setting do?
- It sets how many digits of the coefficient are kept, rounding the last one. At 3 significant figures, 123,456 becomes 1.23 × 105. Choose the precision your measurement or assignment requires.
- How do I multiply and divide numbers in scientific notation?
- To multiply, multiply the coefficients and add the exponents: (2 × 103) × (3 × 104) = 6 × 107. To divide, divide the coefficients and subtract the exponents. If the coefficient ends up outside 1 to 10, shift the point and adjust the exponent.