How to use it
- Choose number to scientific notation or the reverse.
- Enter the number, or the coefficient and exponent.
- Read scientific, engineering and E notation.
- Copy the standard decimal form if you need it.
What scientific notation is
Scientific notation writes a number as a coefficient between 1 and 10 times a power of ten:
a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer
It keeps very large and very small numbers readable and makes their size obvious at a glance.
| Standard form | Scientific notation |
|---|---|
| 300,000,000 | 3 × 10⁸ |
| 0.000123 | 1.23 × 10⁻⁴ |
| 6,022,140,760,000,000,000,000,000 | 6.02214076 × 10²³ |
| 0.0000000001 | 1 × 10⁻¹⁰ |
The calculator converts both ways in your browser and also shows engineering notation and E notation.
How to convert by hand
Large numbers: move the decimal point left until one nonzero digit remains in front. The number of places moved is the positive exponent. 45,600 → 4.56, moved 4 places, so 4.56 × 10⁴.
Small numbers: move the decimal point right until it is just after the first nonzero digit. The number of places is the negative exponent. 0.000123 → 1.23, moved 4 places, so 1.23 × 10⁻⁴.
Back to standard form: move the point the other way. 2.5 × 10⁻³ = 0.0025.
Engineering and E notation
Engineering notation uses exponents that are multiples of 3, which line up with metric prefixes:
| Power | Prefix | Example |
|---|---|---|
| 10⁹ | giga (G) | 2.4 GHz |
| 10⁶ | mega (M) | 12 MP camera |
| 10³ | kilo (k) | 4.7 kΩ resistor |
| 10⁻³ | milli (m) | 250 mA |
| 10⁻⁶ | micro (µ) | 123 µm |
| 10⁻⁹ | nano (n) | 650 nm red light |
0.000123 in engineering notation is 123 × 10⁻⁶. E notation is how calculators and spreadsheets display the same thing: 1.23E-4 means 1.23 × 10⁻⁴. You can type E notation (such as 1.2e9) straight into the input.
Calculating with scientific notation
- Multiply: multiply the coefficients and add the exponents. (3 × 10⁸) × (2 × 10⁻³) = 6 × 10⁵.
- Divide: divide the coefficients and subtract the exponents. (8 × 10⁶) / (4 × 10²) = 2 × 10⁴.
- Add or subtract: first rewrite the numbers with the same exponent. 3 × 10⁴ + 5 × 10³ = 3 × 10⁴ + 0.5 × 10⁴ = 3.5 × 10⁴.
Afterward, normalize the coefficient so it is between 1 and 10. If you enter a coefficient such as 45 in the reverse mode, the calculator normalizes it for you (4.5 × 10¹ more).
Real-world values
- Speed of light: 299,792,458 m/s ≈ 3.00 × 10⁸ m/s
- Avogadro's number: 6.02214076 × 10²³ per mole
- Average distance from Earth to the Sun: about 9.3 × 10⁷ miles
- Mass of an electron: about 9.109 × 10⁻³¹ kg
- Diameter of a human hair: roughly 7 × 10⁻⁵ m
For arithmetic with values like these, the scientific calculator accepts E notation, and the rounding calculator handles significant figures.
Common mistakes
- Wrong sign on the exponent. Numbers smaller than 1 have negative exponents; numbers 10 or larger have positive ones.
- Counting the wrong number of places. 0.00052 is 5.2 × 10⁻⁴, not 10⁻³. Count the moves the decimal point makes.
- Forgetting to normalize. 0.6 × 10⁵ should be written 6 × 10⁴.
- Adding exponents when adding numbers. Exponents are added only when you multiply.
- Losing significant figures. 3.00 × 10⁸ signals three significant figures; 3 × 10⁸ signals one.
Frequently asked questions
How do I write 0.000123 in scientific notation?
1.23 × 10⁻⁴. Move the decimal point four places to the right.
What does E mean on a calculator?
It stands for times ten to the power: 1.23E-4 means 1.23 × 10⁻⁴.
What is the difference between scientific and engineering notation?
Scientific notation uses a coefficient from 1 to 10; engineering notation uses exponents that are multiples of 3, matching metric prefixes.
Can the coefficient be 10 or more?
Not in proper scientific notation. 45 × 10³ should be written 4.5 × 10⁴, and the calculator normalizes it.
Is scientific notation the same as standard form?
In the U.S., standard form usually means the ordinary decimal number. In the UK, standard form means scientific notation.
Last updated: November 12, 2026