Scientific Notation Converter

Convert decimal ↔ scientific notation. Standard form a × 10^b with 1 ≤ |a| < 10.

Inputs

Result

Scientific notation
4.560000 × 10^-4
0.000456.
  • Decimal0.000456
  • Mantissa (a)4.560000
  • Exponent (b)-4
  • Signpositive

Step-by-step

  1. Find e = ⌊log₁₀|v|⌋ = -4.
  2. Mantissa = v / 10^e = 0.000456 / 10^-4 = 4.560000.
  3. Result: 4.560000 × 10^-4.

How to use this calculator

  • Pick direction.
  • Enter values.
  • Calculator normalizes mantissa to 1 ≤ a < 10.

About this calculator

Scientific notation expresses very large or small numbers as a × 10^b with 1 ≤ |a| < 10. 0.000456 = 4.56 × 10⁻⁴; 6.022 × 10²³ = 602,200,000,000,000,000,000,000 (Avogadro's number). Programmers and engineers use "e-notation" (1.5e-4 = 1.5 × 10⁻⁴). For everyday numbers (1 to 10000), it's overkill; for atomic-to-cosmic scales, essential.

Frequently asked

Standard "scientific notation" canonical form. Other normalizations (engineering: exponents only multiples of 3) exist for specific contexts.

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