How to use this calculator
- Enter or choose task.
- Enter or choose significant figures.
- The scientific notation updates as you type. Use Copy result or Share to keep it.
Method
x = a × 10ⁿ with 1 ≤ |a| < 10; engineering notation uses an exponent that is a multiple of 3; (a × 10ᵐ)(b × 10ⁿ) = ab × 10^(m+n)
- a
- the coefficient (mantissa)
- n
- the power of ten
Worked example
- Move the decimal point right until one non-zero digit is in front of it: 0.000456 → 4.56.
- It moved 4 places right, so the exponent is −4: 4.56 × 10⁻⁴.
- For engineering notation use the nearest lower multiple of 3: 456 × 10⁻⁶.
0.000456 is 4.56 × 10⁻⁴ in scientific notation, 4.56e-4 in E notation and 456 × 10⁻⁶ in engineering notation.
What the result means
The exponent shows the order of magnitude and the coefficient’s digits are the significant figures. Engineering notation lines up with SI prefixes: 10³ kilo, 10⁻³ milli, 10⁻⁶ micro.
Assumptions and limits
- Calculations are exact on the decimal digits, except division, which is computed to at least 40 significant digits before rounding.
- Rounding to significant figures is half away from zero.
- Exponents are limited to ±10,000.
Questions
Are trailing zeros significant?
In 0.00045600 the trailing zeros after the decimal point count, giving 4.5600 × 10⁻⁴ (5 significant figures). In a whole number such as 123000 they are ambiguous, so they are not counted unless you set the significant figures.
What does 6.02e23 mean?
E notation is how calculators and programming languages write 6.02 × 10²³.