Scientific notation calculator: convert between decimal, scientific, E and engineering notation, and add, subtract, multiply or divide with sig-fig rules.
By AdminDrafted with AI writing toolsUpdated Checked examples: 10
299792458 is 2.99792458 × 10⁸ in scientific notation, 2.99792458e8 in E notation and 299.792458 × 10⁶ in engineering notation. Significant figures: 9.
299792458 has 9 significant figures.
The point moves 8 places left to sit after the first significant digit, so the exponent is 8.
Engineering notation lowers the exponent to a multiple of 3 (6); E notation writes “× 10^” as e: 2.99792458e8.
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.
Write the number as a × 10ⁿ, with one nonzero digit before the decimal point. Move the point until that is true and count the moves: moving it left gives a positive n, moving it right a negative n. So 45,200 = 4.52 × 10⁴ and 0.000452 = 4.52 × 10⁻⁴.
The sign of the number stays on a, so −0.00057 = −5.7 × 10⁻⁴; a negative exponent means a small number, not a negative one. Zero has no leading nonzero digit and is written 0 × 10⁰.
E notation, used by calculators, spreadsheets and programming languages, replaces "× 10^" with E: 6.02E23 means 6.02 × 10²³. The E has nothing to do with Euler's number e.
Engineering notation keeps the exponent a multiple of 3, so the leading number runs from 1 to under 1,000. That lines the value up with SI prefixes: 0.00057 is 5.7 × 10⁻⁴ in scientific form but 570 × 10⁻⁶, or 570 micro-units, in engineering form.
| Typed number | Scientific | E notation | Engineering |
|---|---|---|---|
| 299792458 | 2.99792458 × 10⁸ | 2.99792458e8 | 299.792458 × 10⁶ |
| 0.005600 | 5.600 × 10⁻³ | 5.600e-3 | 5.600 × 10⁻³ |
| 0.00057 | 5.7 × 10⁻⁴ | 5.7e-4 | 570 × 10⁻⁶ |
| -0.00057 | −5.7 × 10⁻⁴ | -5.7e-4 | −570 × 10⁻⁶ |
| 1200 | 1.2 × 10³ | 1.2e3 | 1.2 × 10³ |
| 1200. | 1.200 × 10³ | 1.200e3 | 1.200 × 10³ |
| 6.02E23 | 6.02 × 10²³ | 6.02e23 | 602 × 10²¹ |
| 5.600 × 10^-3 | 5.600 × 10⁻³ | 5.600e-3 | 5.600 × 10⁻³ |
Scientific notation shows precision as well as size, because every digit of the leading number is significant. Leading zeros only place the decimal point and never count.
Trailing zeros after a decimal point do count, so 0.005600 has four significant figures and becomes 5.600 × 10⁻³.
Trailing zeros in a whole number are ambiguous. 1200 is read as two significant figures, 1.2 × 10³; write 1200. with a final point, or 1.200 × 10³, when all four digits were measured.
Multiply the leading numbers and add the exponents; divide the leading numbers and subtract the exponents. Then move the point again if the leading number has left the range 1 to 10:
With measured values, a product or quotient keeps the fewest significant figures of the inputs. (1.2 × 10⁵) × (3.45 × 10⁻²) is exactly 4,140, but 1.2 has only two significant figures, so the measured result is 4.1 × 10³.
Rewrite both numbers with the same power of ten, then add or subtract the leading numbers. The difference 5.2 × 10⁴ − 3.1 × 10³ becomes 5.2 × 10⁴ − 0.31 × 10⁴ = 4.89 × 10⁴.
For measurements, a sum or difference keeps the least precise decimal place. 5.2 × 10⁴ is known only to the thousands, so that difference is reported as 4.9 × 10⁴. OpenStax Chemistry sets out both rules.
The table uses these operands. Rows marked exact keep every digit; the others apply the significant-figure rules:
| Example | Scientific result | Decimal result |
|---|---|---|
| default multiplication | 4.1 × 10³ | 4,100 |
| exact multiplication | 4.14 × 10³ | 4,140 |
| sum measured | 1.262 × 10⁵ | 126,200 |
| sum exact | 1.26155 × 10⁵ | 126,155 |
| cancellation | 1 × 10⁰ | 1 |
| difference measured | 6.5 × 10¹ | 65 |
| difference exact | 6.477 × 10¹ | 64.77 |
| quotient measured | 4.0 × 10⁶ | 4,000,000 |
The cancellation row shows how subtraction can wipe out precision: two four-figure numbers leave a one-figure answer.
When the dropped part is exactly 5, two conventions disagree. Rounding half up moves away from zero, so 92.85 to three significant figures is 92.9. Rounding half to even, the OpenStax convention, picks the even neighbor, so 92.85 becomes 92.8.
Values beyond an exact tie round normally: 92.851 becomes 92.9 under both rules.
For functions or nested arithmetic, use the scientific calculator, and to round to a decimal place rather than to significant figures, the rounding calculator.
Checked against: SI defining constant c = 299 792 458 m/s (BIPM SI Brochure 9th ed.); notation forms by hand
Checked against: Calculator Soup scientific notation converter: 357,096 = 3.57096 × 10^5
Checked against: Calculator Soup scientific notation converter: 0.005600 = 5.600 × 10^-3, trailing zeros kept as significant
Checked against: Omni Calculator scientific notation page: 0.00057 = 5.7 × 10⁻⁴; engineering form by moving to the next lower multiple of 3
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.
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.
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.
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.
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.
This calculator includes 10 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.