What scientific notation is
Scientific notation writes any number as a mantissa times a power of ten: a × 10^n, where the mantissa a has an absolute value between 1 and 10, and n is a whole number. It is the standard way to handle huge quantities — like the speed of light — or tiny ones — like the size of an atom — without dragging along an endless line of zeros.
This converter works both ways. Type an ordinary decimal number (for instance 0.00042 or 150000) and you instantly get its scientific form, its engineering form, and its E notation. And in reverse: type 4.2e-4 or even 1.5 × 10^5 and it hands you the expanded decimal. Everything is computed in your browser with toExponential, which guarantees a clean, correctly rounded mantissa.
How to use the converter
- Type a value in the field. It accepts decimals (
0.0075), E notation (7.5e-3), and the power form (7.5 × 10^-3). Use a dot as the decimal separator. - Optionally choose the significant figures (1 to 10) to round the mantissa; “Automatic” shows exactly as many as needed to keep the number intact.
- Read the results panel: decimal, scientific, engineering, and E notation all appear at once.
- Press Copy on whichever row you need. The example buttons fill the field with typical cases.
There is no “calculate” button — the result updates as you type.
The three forms and their rules
- Scientific: exactly one non-zero digit before the point. The exponent can be any integer.
- Engineering: same idea, but the exponent is forced to be a multiple of 3, so the mantissa lands between 1 and 1000. This lines up with SI prefixes (kilo =
10^3, mega =10^6, micro =10^-6). - E notation: the same information with the letter
ereplacing× 10^; it is what calculators and programming languages use.
| Decimal | Scientific | Engineering | E notation |
|---|---|---|---|
| 150000 | 1.5 × 10^5 | 150 × 10^3 | 1.5e5 |
| 0.00042 | 4.2 × 10^-4 | 420 × 10^-6 | 4.2e-4 |
| 47000 | 4.7 × 10^4 | 47 × 10^3 | 4.7e4 |
| 299792458 | 2.99792458 × 10^8 | 299.792458 × 10^6 | 2.99792458e8 |
| 0.000000001 | 1 × 10^-9 | 1 × 10^-9 | 1e-9 |
Worked example
Let’s convert 0.00042 to scientific notation. Slide the decimal point to the right until a single non-zero digit sits in front: 0.00042 → 4.2. Count how many places you moved it: four to the right, so the exponent is negative, -4. Scientific result: 4.2 × 10^-4.
For the engineering form the exponent must be a multiple of 3. The nearest one below -4 is -6; we lowered the exponent by two, so the mantissa’s point slides two places to the right: 4.2 → 420. Engineering result: 420 × 10^-6, which also reads as “420 micro-units”.
Check in reverse: 4.2 × 10^-4 = 4.2 × 0.0001 = 0.00042, and 420 × 10^-6 = 420 × 0.000001 = 0.00042. The other classic case: 150000 = 1.5 × 10^5 = 150 × 10^3, with E notation 1.5e5. Both match.
Frequently asked questions
What is the difference between scientific and engineering notation?
In scientific notation the mantissa always has a single integer digit (between 1 and 10) and the exponent is free. In engineering notation the exponent is restricted to multiples of 3, so the mantissa can reach up to 999. That makes it perfect for reading results in kilo, mega, giga, milli, or micro without any extra conversion.
Can I enter a number already in scientific notation?
Yes. The field understands 6.022e23, 4.2E-4, and also the power form 1.5 × 10^5 (with ×, x, or *). The converter reads it and shows you its expanded decimal alongside every other form.
What are significant figures and when should I change them?
They are the informative digits of the mantissa. If you measure to three significant figures, 12345 becomes 1.23 × 10^4. Adjust the selector when your data has a specific precision; leave “Automatic” to keep all the exact digits of the number.
How does it handle zero and negatives?
Zero shows as 0 in every form, with no misleading exponent. Negatives keep the sign in front of the mantissa: -0.0000091 converts to -9.1 × 10^-6. The sign never affects the exponent, it only rides along with the mantissa.
Why a dot and not a decimal comma?
To avoid clashing with thousands separators and to match scientific and programming use. If you type a comma, the tool reads it as a decimal point, but the safest choice is to type the dot directly.