# Scientific Notation Calculator

> Convert numbers to scientific, E and engineering notation, or add, subtract, multiply and divide in scientific notation with significant figures.

Category: Mathematics · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/scientific-notation-calculator

Scientific notation writes a number as a coefficient from 1 to under 10 times a power of ten, such as 4.56 × 10⁻⁴. It keeps very large and very small numbers readable.

Also called: Standard form calculator, Exponential notation converter.

## Inputs
- Task (options: Convert a number, Calculate; default convert)
- Number (default 0.000456)
- First number (default 3e8)
- Operation (options: Add (+), Subtract (−), Multiply (×), Divide (÷); default mul)
- Second number (default 2e-3)
- Significant figures (default ; optional)

## Results
- Scientific notation
- E notation
- Engineering notation
- Decimal form
- Coefficient
- Exponent
- Significant figures shown

## Formula

```
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)
```

Where:
- a: the coefficient (mantissa)
- n: the power of ten

## Worked example
1. Move the decimal point right until one non-zero digit is in front of it: 0.000456 → 4.56.
2. It moved 4 places right, so the exponent is −4: 4.56 × 10⁻⁴.
3. For engineering notation use the nearest lower multiple of 3: 456 × 10⁻⁶.

**Result:** 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.

## Related calculators
- [Rounding Calculator](https://calculators.geekmidst.com/calculators/rounding-calculator)
- [Big Number Calculator](https://calculators.geekmidst.com/calculators/big-number-calculator)
- [Percentage Calculator](https://calculators.geekmidst.com/calculators/percentage-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/scientific-notation-calculator