Scientific Notation Calculator
Convert numbers to/from scientific, engineering and E notation, and multiply or divide in scientific notation.
Inputs
Scientific notation
6.02 × 10^-4
Result (decimal)
0.0000000000
Engineering notation
602 × 10^-6
E notation (code style)
6.020e-4
Coefficient
6.020000
Exponent (power of 10)
-4
Step by step
Input
= 0.000602
Find exponent
floor(log₁₀(|0.000602|)) = -4
= e = -4
Compute coefficient
0.000602 ÷ 10^-4
= a = 6.02
Scientific notation
= 6.02 × 10^-4
Engineering notation (exponent multiple of 3)
= 602 × 10^-6
E notation
= 6.020e-4
How it works
Scientific notation expresses any number as a coefficient between 1 and 10 multiplied by a power of 10. It is compact for very large or very small values and makes multiplication and division easy: multiply the coefficients and add (or subtract) the exponents. Engineering notation uses the same structure but restricts the exponent to multiples of 3 so they align with SI prefixes (kilo-, mega-, giga-, milli-, micro-, etc.).
Formulas
Scientific notation
x = a × 10^e where 1 ≤ |a| < 10
- a
- Coefficient (significand)
- e
- Integer exponent
Multiplication in scientific notation
(a₁ × 10^e₁) × (a₂ × 10^e₂) = (a₁·a₂) × 10^(e₁+e₂)
Frequently Asked Questions
What is the difference between scientific and engineering notation?
Both use a coefficient times a power of 10. Scientific notation forces the coefficient between 1 and 10 (exponent can be any integer). Engineering notation forces the exponent to be a multiple of 3 — so the same number may have a coefficient between 1 and 999. This aligns with SI prefixes: 1 × 10³ = 1 kilo, 1 × 10⁶ = 1 mega, etc.
How do I multiply numbers in scientific notation by hand?
Multiply the coefficients and add the exponents: (3.0 × 10⁴) × (2.0 × 10³) = 6.0 × 10⁷. If the new coefficient is ≥ 10, divide it by 10 and add 1 to the exponent to normalize.
What does 'E notation' mean in a calculator or spreadsheet?
'1.23E+4' means 1.23 × 10⁴ = 12300. It is the text representation used in programming languages, spreadsheets and scientific instruments where superscripts cannot be displayed.