How to use the Scientific Notation Calculator
- Type a number. Small and large values can be entered as 1.5e-6 or 6.02e23.
- Choose how many significant figures to keep.
- Read the number in scientific, engineering and E notation.
- Use the standard form row to turn a long number back into an ordinary decimal.
Formula used
Scientific notation writes a number as a × 10ⁿ with 1 ≤ |a| < 10. Engineering notation uses an exponent that is a multiple of 3. E notation writes a × 10ⁿ as aEn.
Worked example
Here is the Scientific Notation Calculator worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| Number (you can type 1.5e-6) | 123,456,789 |
| Significant figures | 6 |
| Result | |
| Scientific notation | 1.23457 × 10^8 |
| Engineering notation | 123.457 × 10^6 |
| E notation | 1.23457e+8 |
| Standard form | 123,457,000 |
How scientific notation works
A number in scientific notation has the form a × 10^n, where the coefficient a is at least 1 and less than 10 (in absolute value) and n is a whole number. To convert 123,456,789, move the decimal point 8 places left to get 1.23456789 and write × 10^8. Rounded to 6 significant figures, that is 1.23457 × 10^8.
For numbers smaller than 1, the exponent is negative: move the decimal point right until one non-zero digit is before it. So 0.000123 is 1.23 × 10^-4. A positive exponent means a large number, a negative exponent a small one.
Engineering and E notation
Engineering notation always uses an exponent that is a multiple of 3, matching the metric prefixes kilo (10^3), mega (10^6), giga (10^9), milli (10^-3) and micro (10^-6). The same example becomes 123.457 × 10^6, which is 123.457 million. The coefficient can then be between 1 and 1000.
E notation is the plain-text version: 1.23457e+8. The "e" means "times ten to the power of", and it is what calculators, spreadsheets and programming languages print for very large or small values. It is not related to the mathematical constant e.
Significant figures
Significant figures are the digits that carry meaning, counted from the first non-zero digit. The number 0.00450 has three: 4, 5 and 0. Choosing fewer figures rounds the coefficient: with 3 figures, 123,456,789 becomes 1.23 × 10^8. The standard form row shows the rounded number written out: 123,000,000.
In science, the number of figures you write shows how precisely something was measured. Writing 1.50 × 10^3 says you know the value to three figures, while 1.5 × 10^3 says two.
Real-world numbers
The speed of light is about 2.998 × 10^8 metres per second. Avogadro’s number is about 6.022 × 10^23 per mole. The mass of an electron is about 9.109 × 10^-31 kilograms, and the distance from the Earth to the Sun is about 1.496 × 10^11 metres.
To multiply two numbers in scientific notation, multiply the coefficients and add the exponents. To divide, divide the coefficients and subtract the exponents. If the coefficient ends up outside 1 to 10, adjust it and change the exponent to match.
Frequently asked questions
What is 1,000,000 in scientific notation?
1 × 10^6. The decimal point moves six places.
How do I enter a very small number?
Use E notation in the box, such as 3.2e-9 for 0.0000000032.
What is the difference between scientific and engineering notation?
Scientific notation keeps one digit before the decimal point. Engineering notation uses exponents that are multiples of 3, so the coefficient can run from 1 to 999.
What does the e in 1.5e6 mean?
It means "times ten to the power of". So 1.5e6 is 1.5 × 10^6, which is 1,500,000.
How many significant figures should I use?
Match the precision of your data. Three or four is common in school work, and you should not report more digits than you measured.
Can it handle negative numbers?
Yes. The sign stays in front of the coefficient, for example -5 × 10^22.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.