Scientific Notation Calculator
Convert a decimal number to standard scientific notation (m × 10ⁿ), engineering notation, e-notation and SI metric prefixes; convert scientific notation back to decimal; or multiply and divide two numbers written in scientific notation.
Written by Suhaib Hassan. Every rule follows the ISO 80000-1 normalized-form definition. Our methodology.
The mantissa and exponent are extracted from the exact decimal digit string, so rounding to a chosen number of significant figures uses true half-to-even arithmetic, not floating-point approximation.
It shows standard, engineering, e-notation and SI-prefix form side by side, so you can see how they relate.
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Step-by-step working
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SI metric prefixes
Powers of 10 used as unit prefixes.
| Prefix | Symbol | Power of 10 | Prefix | Symbol | Power of 10 |
|---|---|---|---|---|---|
| giga | G | 10⁹ | milli | m | 10⁻³ |
| mega | M | 10⁶ | micro | µ | 10⁻⁶ |
| kilo | k | 10³ | nano | n | 10⁻⁹ |
| (none) | — | 10⁰ | pico | p | 10⁻¹² |
Worked examples
Small decimal
Write 0.00004582 in scientific notation.
4.582 × 10⁻⁵
Multiplying
(6.02×10²³) × (3.2×10⁻⁴)
6.02×3.2=19.264 → renormalize
1.9264 × 10²⁰
Back to decimal
Convert 2.5 × 10⁻³ to decimal.
0.0025
The three notations
- Standard scientific: m × 10ⁿ with exactly one non-zero digit before the decimal point (1 ≤ |m| < 10).
- Engineering notation: the exponent is forced to a multiple of 3, so the mantissa is 1 ≤ |m| < 1000 — this aligns directly with SI prefixes (kilo, mega, milli, …).
- E-notation: the plain-text computing form, m followed by "e" and the exponent, e.g. 4.582e-5 — identical in value to standard scientific notation.
By Suhaib Hassan · Reviewed 29 September 2026 · How CalculatePilot verifies formulas →
Sources
- ISO 80000-1:2022, Quantities and units — Part 1: General, annex on number representation.
- BIPM (2019). The International System of Units (SI) (9th ed.), chapter 3 (SI prefixes).
Frequently asked questions
What's the difference between scientific and engineering notation?
Standard scientific notation always has exactly one digit before the decimal point. Engineering notation instead forces the exponent to a multiple of 3, so the mantissa can have 1, 2 or 3 digits before the point — this matches SI prefixes like kilo (10³) and mega (10⁶) directly.
Why do calculators and programs write "e" instead of "× 10"?
"e" notation (like 4.582e-5) is a plain-text way to write scientific notation without special symbols, used across programming languages, spreadsheets and calculator displays — mathematically it means exactly the same as 4.582 × 10⁻⁵.
How does multiplying in scientific notation work?
Multiply the mantissas and add the exponents: (a×10ᵐ)×(b×10ⁿ) = (a×b)×10ᵐ⁺ⁿ. If the mantissa product is 10 or more (or less than 1), renormalize by shifting the decimal point and adjusting the exponent.
Why use scientific notation at all?
It makes very large or very small numbers compact and easy to compare — and it separates the number's precision (the mantissa's significant figures) from its scale (the exponent), which is why it's the standard in science and engineering.
How is rounding handled when converting?
Using exact half-to-even (banker's) rounding on the digit string itself — not on a floating-point approximation — so results match the textbook rule precisely, including for ties.
How to convert decimals and scientific form: scientific notation guide.
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