Scientific Notation Converter

Scientific notation expresses numbers as a mantissa (a value between 1 and 10, or exactly 1 in engineering notation) multiplied by a power of 10. The speed of light is approximately 3 × 10⁸ meters per second instead of 300,000,000 m/s. A bacterium might measure 2 × 10⁻⁶ meters (0.000002 m) rather than a string of zeros. This compact form prevents errors from miscounting zeros and makes comparisons across vastly different scales straightforward.

To convert a standard number to scientific notation, move the decimal point so exactly one nonzero digit appears to its left. Count how many places you moved — that count is the exponent. Moving left (large numbers) gives a positive exponent: 3,400,000 = 3.4 × 10⁶ (decimal moved 6 places left). Moving right (small numbers) gives a negative exponent: 0.00045 = 4.5 × 10⁻⁴ (decimal moved 4 places right). The mantissa is always between 1 and 10 (or equal to 1 in strict form, or between 1 and 10 exclusive of 10).

Converting from scientific notation to standard form reverses the process. For 5.98 × 10⁵, move the decimal 5 places right: 598,000. For 2.1 × 10⁻³, move 3 places left: 0.0021. On calculators and in programming, the letter "E" or "e" often replaces "× 10^": 3.4E6 means 3.4 × 10⁶. This calculator accepts both formats for input.

Arithmetic in scientific notation leverages exponent rules. To multiply, multiply mantissas and add exponents: (3 × 10⁴)(2 × 10³) = 6 × 10⁷. To divide, divide mantissas and subtract exponents. To add or subtract, first express both numbers with the same exponent, then combine mantissas. These operations are how scientists and engineers handle astronomy distances, atomic measurements, and national debt figures without losing precision.

Significant figures and scientific notation work together in laboratory science. The notation communicates both magnitude and precision — 6.02 × 10²³ (Avogadro's number) has three significant figures. Very large and very small numbers that appear in physics, chemistry, and biology — Planck's constant (6.626 × 10⁻³⁴ J·s), Earth's mass (5.97 × 10²⁴ kg), the diameter of a hydrogen atom (1.06 × 10⁻¹⁰ m) — are naturally expressed this way. Convert any number in either direction using this tool.