Convert numbers between decimal and scientific notation, or perform arithmetic operations (+, −, ×, ÷, ^, √) with high-precision exponents.
Provide a number below to get its scientific notation, E-notation, engineering notation, and real number format. Accepts standard integers (e.g. 3672.2), E-notation (2.3e11), or scientific multiplication (3.5x10^-12).
Scientific notation is a standardized method of writing very large or very small real numbers compactly using base-10 powers. A number in normalized scientific notation is written in the format:
Here, a is called the significand (or coefficient) and b is the exponent. For example, 1,568,938 is written as 1.568938 × 10⁶, and 0.000456 is written as 4.56 × 10⁻⁴.
Standard form with exactly one non-zero digit before the decimal point:
Computer and calculator shorthand where "e" or "E" replaces "× 10^":
Exponents restricted to multiples of 3 (10³, 10⁶, 10⁻³, 10⁻⁶) matching SI prefixes:
Multiply significands, add exponents, and re-normalize.
Divide significands, subtract exponents, and re-normalize.
Align exponents to match before adding or subtracting significands.
Multiply exponents for powers; ensure even exponent before taking square root.
| Prefix | Symbol | Factor | Short Scale Name |
|---|---|---|---|
| Exa | E | 10¹⁸ | Quintillion |
| Peta | P | 10¹⁵ | Quadrillion |
| Tera | T | 10¹² | Trillion |
| Giga | G | 10⁹ | Billion |
| Mega | M | 10⁶ | Million |
| Kilo | k | 10³ | Thousand |
| Base Unit | — | 10⁰ = 1 | One |
| Milli | m | 10⁻³ | Thousandth |
| Micro | µ | 10⁻⁶ | Millionth |
| Nano | n | 10⁻⁹ | Billionth |
| Pico | p | 10⁻¹² | Trillionth |
| Femto | f | 10⁻¹⁵ | Quadrillionth |
Move the decimal point until exactly one non-zero digit is on the left. The number of places moved becomes the exponent: moving left gives a positive exponent (e.g. 1500 ➔ 1.5 × 10³), moving right gives a negative exponent (e.g. 0.015 ➔ 1.5 × 10⁻²).
A negative exponent indicates a value between 0 and 1 (a fraction). For example, 10⁻³ = 1 / 10³ = 1 / 1000 = 0.001.
Engineering notation restricts exponents to multiples of 3, directly matching standard physical SI prefixes such as milli (10⁻³), micro (10⁻⁶), kilo (10³), and mega (10⁶).