Scientific Notation Converter Calculators

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Scientific notation is a compact way to express very large or very small numbers as a product of a number between 1 and 10 and a power of 10: a × 10^n. It is indispensable in science for managing the enormous range of magnitudes encountered — from the diameter of a hydrogen atom (1.06 × 10⁻¹⁰ m) to the number of molecules in a mole (6.022 × 10²³). Scientific notation simplifies arithmetic, reduces transcription errors, and makes the magnitude of numbers immediately apparent. Every scientific and engineering field uses scientific notation extensively.

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Scientific Notation Format

a × 10^n where 1 ≤ a < 10 and n is any integer.

Converting to Scientific Notation

Large Numbers

Move the decimal point left until one non-zero digit is before it. Count the places moved — that is n (positive).

45,700,000 → 4.57 × 10⁷ (moved 7 places left)

Small Numbers (Decimals)

Move the decimal point right until one non-zero digit is before it. Count the places moved — n is negative.

0.0000348 → 3.48 × 10⁻⁵ (moved 5 places right)

Converting from Scientific Notation

3.21 × 10⁴: move decimal 4 places right → 32,100
7.6 × 10⁻³: move decimal 3 places left → 0.0076

Arithmetic in Scientific Notation

Multiplication

(a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n)

(3.0 × 10⁴) × (2.5 × 10³) = 7.5 × 10⁷

Division

(a × 10^m) / (b × 10^n) = (a/b) × 10^(m−n)

(8.0 × 10⁸) / (4.0 × 10³) = 2.0 × 10⁵

Addition/Subtraction

Convert to the same exponent first:
(3.0 × 10⁴) + (5.0 × 10³) = 3.0 × 10⁴ + 0.5 × 10⁴ = 3.5 × 10⁴

Scientific Prefixes (SI)

  • 10⁻¹² = pico (p)
  • 10⁻⁹ = nano (n)
  • 10⁻⁶ = micro (μ)
  • 10⁻³ = milli (m)
  • 10³ = kilo (k)
  • 10⁶ = mega (M)
  • 10⁹ = giga (G)
  • 10¹² = tera (T)

Glossary

Scientific Notation
A compact representation of numbers as a × 10^n where 1 ≤ a < 10 and n is an integer. Makes very large or small numbers manageable and arithmetic simpler. To multiply: multiply coefficients, add exponents. To divide: divide coefficients, subtract exponents.
Coefficient
In scientific notation a × 10^n, the coefficient is a — the number between 1 and 10. Encodes the significant figures of the measurement.
SI Prefix
Standard multipliers attached to SI units representing powers of 10. Examples: nano (10⁻⁹), micro (10⁻⁶), milli (10⁻³), kilo (10³), mega (10⁶), giga (10⁹). Allow expression of measurements without scientific notation for common ranges.

Frequently Asked Questions

Move the decimal point until only one non-zero digit is to the left of it. Count the spaces moved: moving left gives a positive exponent; moving right gives a negative exponent. Examples: 302,000 → 3.02 × 10⁵ (decimal moved 5 left); 0.00047 → 4.7 × 10⁻⁴ (decimal moved 4 right). The coefficient must satisfy 1 ≤ a < 10.

Multiply the coefficients and add the exponents: (a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n). If the result coefficient ≥ 10, adjust: move decimal one place left and increase exponent by 1. Example: (4.0 × 10⁵) × (3.0 × 10⁴) = 12.0 × 10⁹ = 1.2 × 10¹⁰. For division: divide the coefficients and subtract the exponents.

Science deals with numbers spanning extraordinary ranges: the mass of an electron (9.11 × 10⁻³¹ kg) to the mass of the Sun (2.0 × 10³⁰ kg) — a range of 10⁶¹. Writing these as ordinary decimals would be impractical and error-prone. Scientific notation: makes magnitude immediately obvious; simplifies arithmetic with large exponents; reduces transcription errors; and communicates precision through significant figures in the coefficient.

The number of significant figures equals the number of digits in the coefficient. 3.14 × 10⁵ has 3 significant figures; 3.140 × 10⁵ has 4 (the trailing zero after the decimal is significant). Scientific notation eliminates ambiguity about whether zeros are significant: 3,000 could mean 1–4 sig figs, but 3.000 × 10³ unambiguously has 4. When multiplying: result has sig figs = least precise factor. When adding: align decimal places in the coefficients after converting to the same power of 10.