Scientific Notation Calculator
Scientific notation is the standard way to write very large or very small numbers by expressing them as a coefficient multiplied by a power of 10. The form is a * 10^n, where the coefficient a satisfies 1 <= |a| < 10 and n is an integer exponent. For example, the speed of light is 300,000,000 m/s, which is 3.0 * 10^8 in scientific notation. This calculator converts between standard decimal form and scientific notation in both directions. Enter a number to convert it to scientific notation, or enter a coefficient and exponent to compute the standard decimal value.
Scientific notation conversion
Number = a * 10^n, where 1 <= |a| < 10
n = floor(log10(|number|))
a = number / 10^n
The exponent n is the floor of the base-10 logarithm of the absolute value of the number. The coefficient a is then the number divided by 10^n. For negative numbers, the sign is preserved in a.
Scientific notation in science
- Speed of light: 3.0 * 10^8 m/s
- Avogadro's number: 6.022 * 10^23 mol^(-1)
- Electron mass: 9.109 * 10^(-31) kg
- Planck's constant: 6.626 * 10^(-34) J s
- Distance to Andromeda galaxy: approximately 2.4 * 10^22 m
Scientific notation: frequently asked questions
What is scientific notation?
Scientific notation expresses a number as a * 10^n, where 1 <= |a| < 10 and n is an integer. For example, 0.000045 = 4.5 * 10^(-5) and 3,200,000 = 3.2 * 10^6. It is a standard way to represent very large or very small numbers compactly.
How do you convert a number to scientific notation?
Move the decimal point until one non-zero digit is to the left of it. The number of places moved is the exponent n (positive if moved left, negative if moved right). The resulting value with the decimal point in its new position is the coefficient a.
What is E notation?
E notation (used in computing and calculators) writes a * 10^n as aEn. For example, 3.2E6 means 3.2 * 10^6 = 3,200,000 and 4.5E-5 means 4.5 * 10^(-5) = 0.000045. It is equivalent to scientific notation but avoids superscripts.
What is the significance of the coefficient in scientific notation?
The coefficient a (also called the significand or mantissa) carries the significant digits. The number of significant figures is determined by the precision of a. For example, 6.022 * 10^23 has four significant figures in the coefficient.
When is scientific notation used?
Scientific notation is used whenever numbers are very large (e.g., the speed of light: 3.0 * 10^8 m/s) or very small (e.g., electron mass: 9.109 * 10^(-31) kg). It is standard in physics, chemistry, astronomy, and engineering.
Official sources
- NIST Guide to SI Units (NIST SP 811): nist.gov/pml/special-publication-811.
- NIST Physical Constants reference data: physics.nist.gov/cuu/Constants/.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.