🔬Scientific Notation Calculator
Convert any number to scientific notation (a × 10ⁿ), E-notation (aEn), and engineering notation. Accepts decimal numbers, E-notation, and multiplication form (3*10^4). Shows coefficient, exponent, significant figures, and SI unit prefix. Supports significant figures adjustment up to 15 digits.
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Scientific Notation
3 × 10⁴
Powers of 10 Context (|exponent|)
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Scientific Notation Calculator: Convert Numbers to and from Standard Form
Scientific notation expresses any number as a × 10ⁿ where 1 ≤ |a| < 10 and n is an integer. It makes very large or very small numbers compact and easy to compare. The speed of light c = 299,792,458 m/s = 2.998 × 10⁸ m/s. An electron's charge = 0.0000000000000000001602 C = 1.602 × 10⁻¹⁹ C.
Rule: Move decimal left → positive exponent | Move decimal right → negative exponent
| Number | Scientific Notation | E-Notation |
|---|---|---|
| 6,022,000,000,000,000,000,000,000 | 6.022 × 10²³ | 6.022e23 |
| 0.000000000000000000001602 | 1.602 × 10⁻²¹ | 1.602e-21 |
| 0.0045 | 4.5 × 10⁻³ | 4.5e-3 |
Scientific notation is essential in physics, chemistry, astronomy, and computing because the numbers involved span dozens of orders of magnitude: from the Planck length (1.6 × 10⁻³⁵ m) to the observable universe (8.8 × 10²⁶ m).
How to Convert to Scientific Notation
To convert a positive number to scientific notation: (1) Identify where the decimal point is. (2) Move it left or right until you have a number between 1 and 10. (3) The exponent equals the number of places moved — positive if you moved left (large number), negative if you moved right (small number). Example: 45,000: move decimal 4 places left → 4.5; exponent = +4; result: 4.5 × 10⁴. Example: 0.00032: move decimal 4 places right → 3.2; exponent = −4; result: 3.2 × 10⁻⁴.
E-Notation and Engineering Notation
E-notation (used in calculators and computer code) replaces "× 10" with "E": 4.5 × 10⁴ = 4.5E4 = 4.5e4. Engineering notation is a variant where the exponent is always a multiple of 3, aligning with SI prefixes. 45,000 = 45 × 10³ (45 kilo); 0.00045 = 450 × 10⁻⁶ (450 micro). This makes the notation directly readable in SI units: 45 km, 450 μm. The common SI prefixes cover exponents from 10⁻²⁴ (yocto) to 10²⁴ (yotta).
Significant Figures in Scientific Notation
Scientific notation makes significant figures explicit: the number of digits in the coefficient is exactly the number of significant figures. 3 × 10⁴ = 1 sig fig (we only know the leading digit). 3.00 × 10⁴ = 3 sig figs (we know to the hundreds place). This is the primary advantage over decimal notation: "30,000" is ambiguous (1–5 sig figs), while "3.00 × 10⁴" unambiguously means 3 sig figs. Adjust the "Significant Figures" input to round the coefficient to the desired precision.
Frequently Asked Questions
How do I convert a number to scientific notation?
Move the decimal point until the number is between 1 and 10, then multiply by 10 raised to the number of places moved (positive if you moved left, negative if right). Example: 0.00456 → move decimal 3 places right to get 4.56; exponent = −3; result: 4.56 × 10⁻³. Example: 1,234,000 → move decimal 6 places left to get 1.234; exponent = +6; result: 1.234 × 10⁶. For negative numbers: apply the same rules to the absolute value and keep the negative sign: −0.0087 = −8.7 × 10⁻³.
What is the difference between scientific and engineering notation?
Both use the form a × 10ⁿ. Scientific notation: any exponent n is allowed, with 1 ≤ |a| < 10. Engineering notation: n must be a multiple of 3 (0, ±3, ±6, ±9, ...) and a can range from 1 to 999. Example: 25,400 in scientific notation = 2.54 × 10⁴, but in engineering notation = 25.4 × 10³ (25.4 kilo). Engineering notation aligns with SI prefixes (kilo, mega, giga, milli, micro, nano), making it more practical in electrical engineering and physics for attaching unit prefixes directly.
What is E-notation (like 3e4)?
E-notation is computer shorthand for scientific notation: "3e4" means 3 × 10⁴ = 30,000. The "e" (or "E") stands for "× 10 to the power of." Examples: 1.5e-6 = 1.5 × 10⁻⁶ = 0.0000015; 6.022e23 = 6.022 × 10²³ (Avogadro's number). E-notation is used in most programming languages (Python, JavaScript, C), scientific calculators (displaying as 3.14E7), and spreadsheets. It cannot represent numbers in engineering notation directly — you always get exactly one digit before the decimal point in the exponent representation.
How does scientific notation relate to significant figures?
Scientific notation makes significant figures unambiguous. The coefficient in a × 10ⁿ contains exactly the number of significant figures: 3 × 10⁴ → 1 sig fig; 3.0 × 10⁴ → 2 sig figs; 3.00 × 10⁴ → 3 sig figs. This resolves the ambiguity in "30,000" (unknown sig figs) or "0.00400" (3 sig figs, but unclear without context). In measurements and experimental results, always expressing values in scientific notation prevents misinterpretation of precision. The trailing zeros in the coefficient are always significant in scientific notation.