Scientific Notation Calculator
Type a number in almost any form and this scientific notation calculator rewrites it as a × 10ⁿ, in E notation (the format calculators and spreadsheets use) and in engineering notation, where the exponent is a multiple of 3. It also expands the number back to ordinary decimal form, shows the coefficient and exponent separately, and can round the result to the number of significant figures you choose.
Updated
Results
- E notationAs shown by calculators and spreadsheets
- Engineering notationExponent is a multiple of 3
- Decimal formShown when the exponent is between −30 and 30
- CoefficientThe a in a × 10ⁿ
- ExponentThe n in a × 10ⁿ
- Significant figuresFrom your input, or the number you set
Results are estimates. See the methodology below.
How to use the calculator
- Enter the number. All of these work:
0.000004056,1,234,567,6.02e23,6.02E-5,6.02 × 10^23or6.02*10^23. Negative numbers are fine. - Use a period for decimals. Commas are read as thousands separators when they split the digits into groups of three.
- Optionally set significant figures (1 to 15). Leave the field empty to keep the precision of what you typed.
- Read the results: scientific notation first, then E notation, engineering notation, decimal form, coefficient, exponent and the number of significant figures used.
How the conversion works
A number in scientific notation is written as a × 10ⁿ, where the coefficient a satisfies 1 ≤ |a| < 10 and n is an integer. To get there, move the decimal point until exactly one nonzero digit sits in front of it. Each place you move it to the left adds 1 to the exponent; each place to the right subtracts 1. For 0.000004056 the point moves six places right, so n = −6.
The calculator works on the digits you typed rather than on a floating-point approximation, so long inputs such as 24-digit integers keep every digit.
- E notation replaces × 10ⁿ with e followed by the exponent: 4.056e-6.
- Engineering notation uses exponents that are multiples of 3, so the coefficient falls between 1 and 999. Those exponents line up with SI prefixes such as kilo (10³), mega (10⁶), milli (10⁻³) and micro (10⁻⁶).
- Decimal form is shown when the exponent is between −30 and 30.
Significant figures
Leading zeros never count. Trailing zeros count only when the number has a decimal point: 1200 is treated as 2 significant figures, 1200.0 as 5. When you set a number of significant figures, the coefficient is rounded half up, and padded with zeros if you ask for more digits than you entered.
Examples
| Input | Sig. figs | Scientific | E notation | Engineering |
|---|---|---|---|---|
| 0.000004056 | 4 | 4.056 × 10⁻⁶ | 4.056e-6 | 4.056 × 10⁻⁶ |
| 45600 | 3 | 4.56 × 10⁴ | 4.56e+4 | 45.6 × 10³ |
| 0.00980 | 3 | 9.80 × 10⁻³ | 9.80e-3 | 9.80 × 10⁻³ |
| -0.0005 | 1 | -5 × 10⁻⁴ | -5e-4 | -500 × 10⁻⁶ |
Rounding a large number
Enter 602,214,076,000,000,000,000,000 and the calculator returns 6.02214076 × 10²³ with 9 significant figures. Set significant figures to 4 and you get 6.022 × 10²³, or 6.022e+23, or 602.2 × 10²¹ in engineering notation.
Rounding that changes the exponent
9.996 rounded to 2 significant figures becomes 1.0 × 10¹: the coefficient rounds up to 10, so it is rewritten as 1.0 and the exponent goes up by one.
Very small numbers
1.5e-31 stays 1.5 × 10⁻³¹. The decimal form is left out because it would need 30 zeros after the point.
Reading the results
The exponent tells you the order of magnitude: each step of 1 is a factor of 10, so 10⁻⁶ is a thousand times smaller than 10⁻³. The coefficient carries the precision. Writing 1.20 × 10³ instead of 1.2 × 10³ signals that you measured to three significant figures, a distinction plain 1200 can't show.
Frequently asked questions
How do I write a small decimal in scientific notation?
Move the decimal point right until one nonzero digit is in front of it, and count the moves. That count, made negative, is the exponent. 0.00980 needs three moves, giving 9.80 × 10⁻³.
What does the e mean in a number like 4.056e-6?
It is E notation, a plain-text way to write × 10 to the power. 4.056e-6 means 4.056 × 10⁻⁶, and 6.022e+23 means 6.022 × 10²³. Calculators, spreadsheets and programming languages use it because superscripts are hard to type.
What is the difference between scientific and engineering notation?
Scientific notation keeps exactly one digit before the decimal point. Engineering notation lets the coefficient run from 1 to 999 so the exponent is always a multiple of 3, matching SI prefixes: 45.6 × 10³ m reads directly as 45.6 km.
How many significant figures does 1200 have?
It is ambiguous, which is why scientific notation helps. This calculator treats trailing zeros without a decimal point as not significant, so 1200 has 2. Type 1200.0 for 5, or set the significant figures field to the precision you actually have.
Can I enter a number that is already in scientific notation?
Yes. Type it as 6.02e23, 6.02 × 10^23, 6.02x10^23 or 6.02*10^23 and the calculator will normalize it, convert it to the other formats and round it if you ask.
Sources
Results follow the conventions described on this page. If your course or style guide uses a different rule for significant figures or rounding, follow that rule.