Scientific notation
Convert a number to scientific (exponential) notation and back.
Co je scientific notation
Scientific (exponential) notation expresses a number as a × 10ⁿ, where a is between 1 and 10 and n is an integer. It makes very large and very small numbers easy to write.
Where it is used in practice
- Physics and astronomy: the Earth–Sun distance is 1.496 × 10¹¹ m.
- Chemistry: Avogadro’s constant is 6.022 × 10²³ particles per mole.
- Electronics and IT: file sizes, frequencies, chip dimensions.
Good to know
A positive exponent moves the decimal point right (large numbers), a negative one left (small numbers). 3 × 10⁻⁴ = 0.0003.
Rules of exponents
When working with powers it helps to know the basic rules, which always hold:
xⁿ · xᵖ = xⁿ⁺ᵖ (product – add the exponents)
xⁿ ÷ xᵖ = xⁿ⁻ᵖ (quotient – subtract the exponents)
(xⁿ)ᵖ = xⁿ·ᵖ (power of a power – multiply)
x⁻ⁿ = 1 / xⁿ (negative exponent)
x^(1/n) = ⁿ√x (root as a power)
In detail with examples: rules of exponents.
Tip: very large numbers are shown in shortened form – use scientific notation.