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How to use
Scientific notation writes a value as a coefficient times a power of ten. Enter ordinary decimals or E notation such as 6.022e23, optionally perform arithmetic with a second value, and view scientific, E and engineering forms together. In engineering notation, the exponent is a multiple of three. For example, 123,456 = 123.456 × 10³, whereas its scientific form is 1.23456 × 10⁵. Negative values keep their sign: −0.0000047 = −4.7 × 10⁻⁶. Compare both displayed forms to check that the representation preserves the number.
- Enter the first value as a decimal or E-notation number.
- Choose convert-only or an arithmetic operation and provide the second value if needed.
- Calculate to view equivalent scientific, E and engineering forms.
How it is calculated
Example
Example: 0.00042 is 4.2 × 10^-4 and 4.2e-4. In engineering notation it is 420 × 10^-6 because the exponent must be divisible by three.
Important notes
The calculator uses JavaScript floating-point numbers, so it is intended for general calculation rather than arbitrary-precision decimal or symbolic work. Values outside the supported numeric range are rejected. Significant-figure rules are not applied automatically.
Worked examples and interpreting results
Scientific notation separates a number into a coefficient and a power of ten. 45000 becomes 4.5×10⁴, and 0.0045 becomes 4.5×10⁻³. A negative exponent locates the decimal point; it does not make the number negative.
| Case | Calculation | Result |
|---|---|---|
| Large number | 4.5 × 10⁴ | 45,000 |
| Small positive number | 4.5 × 10⁻³ | 0.0045 |
| Engineering form of 45000 | 45 × 10³ | 45,000 |
| Engineering coefficient for 123456 at exponent 3 | 123456 ÷ 10³ | 123.456 |
| Engineering coefficient for −0.0000047 at exponent −6 | −0.0000047 ÷ 10⁻⁶ | -4.7 |
How to check the result
For a nonzero number, a scientific coefficient has absolute value from 1 up to but excluding 10. Engineering notation uses exponents divisible by 3. Writing 4.5e4 means 4.5×10⁴, not multiplication by the constant e.
Scientific notation and powers of ten
Scientific notation writes each nonzero number as a coefficient with absolute value from 1 to below 10 multiplied by ten to an integer exponent.
- 123000 in scientific notation: 123000 = 1.23 × 10⁵ = 1.23 × 10⁵
- 0.00045 in scientific notation: 0.00045 = 4.5 × 10⁻⁴ = 4.5 × 10⁻⁴
- Expand 4.56 × 10³: 4.56 × 1000 = 4560
Important note
Negative exponents represent small nonzero magnitudes. Zero is a special case, and engineering notation uses multiples of three.
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Frequently asked questions
What is E notation?
It is a keyboard-friendly form of ×10^n; for example 3.5e6 means 3.5 × 10^6.
How is engineering notation different?
Scientific notation normalizes the coefficient to magnitude 1–10; engineering notation makes the exponent a multiple of three.
Can I divide by zero?
No. The calculator returns an error instead of an undefined result.
How do I convert scientific notation to engineering notation?
Choose an exponent divisible by three and rescale the coefficient to preserve the value. For example, 1.23456 × 10⁵ becomes 123.456 × 10³. For a nonzero value, the coefficient magnitude is at least 1 and below 1,000.