Scientific Notation Calculator

Free online Scientific Notation Calculator with step-by-step solutions. Convert between decimal, scientific, E, and engineering notation instantly. 100% client-side, no data upload.

Converter

Enter a number

Accepts decimals, E-notation (e.g. 2.3e11), or scientific (e.g. 3.5x10^-12)

Real number—

Scientific notation—

Engineering notation—

E-notation—

Arithmetic

X =

× 10

Y =

× 10

Precision (digits after decimal)

digits

Result—

Scientific notation—

Recent Calculations

No calculations yet.

Scientific Notation Calculator

⚡ Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is written as \(b \times 10^n\), where \(b\) is the significand and \(n\) is the exponent.

What is Scientific Notation? Scientific notation is a compact way to represent very large or very small numbers. The standard form is \(b \times 10^n\) where \(1 \le |b| < 10\) and \(n\) is an integer. For example, \(3.2 \times 10^5\) represents 320,000, and \(4.56 \times 10^{-3}\) represents 0.00456. The significand contains the significant digits, and the exponent indicates the position of the decimal point.

Variants: E-notation & Engineering E-notation replaces the "× 10" with "E", e.g., \(3.2 \times 10^5\) becomes 3.2E5. Engineering notation restricts the exponent to multiples of 3 (e.g., 0, 3, 6, 9, −3, −6), aligning with SI prefixes (kilo, mega, milli, etc.). For example, \(123.4 \times 10^6\) is engineering notation for 123,400,000.

Arithmetic Rules

Addition/Subtraction: Convert to same power of 10, then add/subtract significands: \(a \times 10^n + b \times 10^n = (a + b) \times 10^n\)
Multiplication: Multiply significands, add exponents: \((a \times 10^n) \times (b \times 10^m) = (a \times b) \times 10^{n+m}\)
Division: Divide significands, subtract exponents: \((a \times 10^n) \div (b \times 10^m) = (a \div b) \times 10^{n-m}\)
Power: Raise significand to power, multiply exponent: \((a \times 10^n)^m = a^m \times 10^{n \cdot m}\)

Historical Development

Archimedes (c. 250 BC) — used a form of scientific notation in The Sand Reckoner.
René Descartes (1637) — introduced modern exponent notation.
John Wallis (1655) — first used negative exponents.
Isaac Newton (1669) — used scientific notation in the binomial theorem.
Simon Newcomb (1870s) — advocated for scientific notation in astronomy and physics.

SI Prefixes & Engineering Notation Engineering notation uses exponents that are multiples of 3: 10¹² (tera), 10⁹ (giga), 10⁶ (mega), 10³ (kilo), 10⁰ (base), 10⁻³ (milli), 10⁻⁶ (micro), 10⁻⁹ (nano), 10⁻¹² (pico).

Real-World Applications

Astronomy — distances to stars, mass of planets.
Physics — particle masses, Planck's constant, speed of light.
Chemistry — Avogadro's number, molar masses.
Engineering — circuit values, signal amplitudes.
Computer science — floating-point representation, data sizes.

Precision & Significant Figures In scientific notation, the number of significant figures in the significand reflects the precision. For example, \(3.20 \times 10^5\) has three significant figures. When performing arithmetic, the result should be rounded to the same number of significant figures as the least precise input.

🔒 Client-side only⚡ Web Worker processing🌐 Works offline🛡️ Zero server logs

Frequently Asked Questions

Got questions about scientific notation? We've got answers.

What is scientific notation?

Scientific notation expresses numbers as b × 10ⁿ, where 1 ≤ |b| < 10 and n is an integer. It simplifies working with very large or very small numbers.

What is the difference between scientific and engineering notation?

Engineering notation restricts the exponent to multiples of 3 (like 10³, 10⁶, 10⁻³), aligning with SI prefixes (kilo, mega, milli).

What is E-notation?

E-notation replaces '× 10' with 'E', e.g. 3.2E5 = 3.2 × 10⁵. It is commonly used in programming and calculators.

How do I use the arithmetic panel?

Enter the coefficient and exponent for X and Y, set your desired precision, and click an operation button (+, −, ×, /, ^, √, ²).

Is this calculator private?

Yes. All calculations run locally in your browser. No data is transmitted or stored on any server.