How to write a number in scientific notation
Scientific notation writes a number as a coefficient from 1 up to (but not including) 10, times a power of ten:
number = a × 10n, where 1 ≤ |a| < 10 and n is a whole number
Move the decimal point until one nonzero digit is in front of it. The number of places you moved it is the exponent: positive if you moved it left (a big number), negative if you moved it right (a small number).
Worked examples
- 123,000 → move the point 5 places left → 1.23 × 10⁵. In E notation that's 1.23E5; in engineering notation, 123 × 10³.
- 0.000456 → move it 4 places right → 4.56 × 10⁻⁴, or 456 × 10⁻⁶ in engineering notation (456 micro-).
- 6.02 × 10²³ written out is 602,000,000,000,000,000,000,000.
Arithmetic in scientific notation
- Multiply: multiply the coefficients and add the exponents. (3 × 10⁴) × (2 × 10⁵) = 6 × 10⁹.
- Divide: divide the coefficients and subtract the exponents. (8 × 10⁶) ÷ (2 × 10²) = 4 × 10⁴.
- Add or subtract: first rewrite one number so both have the same exponent. 2.5 × 10³ + 4.1 × 10² = 2.5 × 10³ + 0.41 × 10³ = 2.91 × 10³.
- If the coefficient ends up 10 or more (or below 1), shift it: 12 × 10⁹ = 1.2 × 10¹⁰.
Engineering notation and SI prefixes
Engineering notation keeps the exponent a multiple of 3, so it lines up with metric prefixes: 10³ is kilo (k), 10⁶ mega (M), 10⁹ giga (G), 10⁻³ milli (m), 10⁻⁶ micro (µ) and 10⁻⁹ nano (n). 4.7 × 10⁻⁶ farads is 4.7 µF.
Limits
- A whole number with trailing zeros, like 1200, has ambiguous significant figures. By the usual rule it's treated as 2 (1.2 × 10³). Enter the significant figures you mean, or type 1200. with a decimal point.
- Division results are shown to 15 significant figures, marked ≈ when they don't end.
- Exponents can go from −10,000 to 10,000.