Scientific notation, E notation, and engineering notation
Scientific notation writes a nonzero number as a coefficient with magnitude from 1 up to—but not including—10 multiplied by an integer power of ten.
Engineering notation restricts the exponent to a multiple of three, which aligns naturally with SI prefixes such as kilo, micro, and giga.
How to use the scientific notation converter
- Enter a number: Use ordinary decimal form or E notation such as 6.02e23.
- Choose precision: Select 1 through 15 significant figures for the converted result.
- Convert: Review scientific, E, engineering, SI-prefix, and expanded decimal forms.
- Calculate if needed: Use the arithmetic mode to add, subtract, multiply, or divide two scientific-notation numbers.
Formula and variables
Move the decimal point until the coefficient is normalized. Moving left produces a positive exponent; moving right produces a negative exponent.
N = a × 10ⁿ, where 1 ≤ |a| < 10- N — Original number
- Decimal or E-notation input
- a — Coefficient
- Normalized significand or mantissa
- n — Exponent
- Whole-number power of ten
Convert a small decimal
Write 0.00045 in scientific and engineering notation.
- Number
- 0.00045
- Move the decimal four places right to obtain 4.5.
- A rightward move gives exponent −4.
Result: Scientific: 4.5 × 10⁻⁴; engineering: 450 × 10⁻⁶.
The engineering exponent −6 corresponds to the micro (µ) prefix.
Understanding your results
Equivalent ways to write the same value
Scientific, E, engineering, SI-prefix, and expanded decimal forms differ in notation but represent the same quantity.
- Scientific notation normalizes the coefficient to 1 ≤ |a| < 10.
- Engineering notation uses exponents divisible by three.
- E notation is a plain-text form commonly accepted by calculators and software.
Assumptions
- The exponent is an integer.
- SI-prefix output uses decimal SI prefixes rather than binary prefixes.
Limitations
- Arithmetic uses floating-point mantissas and is not an arbitrary-precision decimal engine.
- Very long standard-form expansions are intentionally suppressed to protect page responsiveness.
- SI-prefix output is limited to the current range from quecto (10⁻³⁰) to quetta (10³⁰).
Common mistakes
- Using a positive exponent for a small decimal less than one.
- Failing to normalize a scientific-notation coefficient.
- Adding coefficients before aligning exponents.
- Confusing lowercase milli m with uppercase mega M.
Practical use cases
Science coursework
Convert measurements and check calculations across very large or small scales.
Engineering communication
Translate powers of ten into engineering notation and recognized SI prefixes.
Frequently asked questions
Is E notation the same as scientific notation?
It represents the same value in a keyboard-friendly form: 6.02e23 means 6.02 × 10²³.
What is the difference between scientific and engineering notation?
Scientific notation uses a coefficient from 1 to less than 10. Engineering notation uses an exponent divisible by three and a coefficient from 1 to less than 1000.
Sources and review
- NIST Guide to the SI, Chapter 4: SI Prefixes — National Institute of Standards and Technology. Accessed 2026-07-14.
Reviewed 2026-07-14.