Scientific Notation Calculator
Use this scientific notation calculator to convert any number to scientific, E, engineering or standard form, and to add, subtract, multiply, divide or raise numbers to a power with clear steps. It uses exact decimal math, so you never see floating-point errors.
- Converter + calculator
- Steps shown
- Significant figures
- Free, no sign-up
Type a decimal, E notation (6.02e23) or 3.2 x 10^5. Commas and spaces are fine.
That is not a number we can read. Try 0.00045, 4.5e-4 or 4.5 x 10^-4.
Auto keeps the significant figures you typed.
Scientific notation
4.56 × 107
3 significant figures · order of magnitude 7
Move the decimal point 7 places left to get 4.56, so the exponent is 7.
Enter a number such as 4.5e6 or 4.5 x 10^6.
Enter a number such as 4.5e6 or 4.5 x 10^6.
Result
3.65 × 105
365,000
Steps
- 3.2 × 105 + 4.5 × 104
Why this scientific notation calculator is more accurate
Many online converters use floating-point numbers, so they show results like 0.30000000000000004. This tool uses exact decimal math and explains every step.
Exact decimal math
Addition, subtraction, multiplication and whole-number powers are exact. Division is precise to 30 significant figures.
Five formats at once
See scientific, E, engineering, SI prefix and standard form together, each with its own copy button.
Clear working
Each calculation shows the rule used, so students can follow and check the method.
Significant figures built in
It counts significant figures and applies the standard rounding rules for each operation.
Reads any format
Type 6.02e23, 3.2 x 10^5, 3.2 × 10⁵ or 45,600,000. The parser understands them all.
Private and shareable
Everything runs in your browser. Share a link that reopens your exact numbers.
How to use the scientific notation calculator
Choose the Converter or Calculator tab, then follow these steps.
- Enter your numberType it in any format, such as 0.00045, 4.5e-4 or 4.5 x 10^-4.
- Pick significant figuresKeep Auto to match what you typed, or round to a set number of figures.
- Read every formatThe result shows scientific, E, engineering, SI prefix and standard form at once.
- Do the mathOn the Calculator tab, enter two numbers and choose add, subtract, multiply, divide or power.
- Check the steps and copyFollow the worked steps, then copy the answer or share a link.
How to convert a number to scientific notation
Scientific notation writes a number as a coefficient from 1 to just under 10, multiplied by a power of 10. It keeps very large and very small numbers short and easy to compare.
First, move the decimal point until exactly one non-zero digit sits to its left. Next, count how many places you moved it. Finally, use that count as the exponent. It is positive when you move the point left and negative when you move it right.
Worked example: 0.000452
- Move the decimal point right until one digit is left of it
- 4.52
- Places moved
- 4 to the right
- Exponent
- −4
- Answer
- 4.52 × 10−4
Multiplying, dividing, adding and subtracting
To multiply, multiply the coefficients and add the exponents. To divide, divide the coefficients and subtract the exponents. However, to add or subtract, you must first rewrite both numbers with the same exponent. Then combine the coefficients and normalize the result so the coefficient is between 1 and 10.
Scientific, E, engineering and standard notation
The same number can be written in several ways. Here is 45,600,000 in each format.
| Format | Example | Rule |
|---|---|---|
| Scientific notation | 4.56 × 107 | Coefficient from 1 to under 10 |
| E notation | 4.56e7 | E means × 10 to the power |
| Engineering notation | 45.6 × 106 | Exponent is a multiple of 3 |
| SI prefix | 45.6 M | Prefix replaces the power of 10 |
| Standard form (decimal) | 45,600,000 | All digits written out |
In the UK, “standard form” often means scientific notation itself. In the US, it usually means the full decimal number.
Common numbers in scientific notation
Well-known values from physics and everyday science, written in scientific notation.
| Quantity | Scientific notation | Unit |
|---|---|---|
| Speed of light | 2.99792458 × 108 | m/s |
| Avogadro constant | 6.02214076 × 1023 | per mol |
| Mass of the Earth | 5.972 × 1024 | kg |
| Earth to Sun distance | 1.496 × 1011 | m |
| One light-year | 9.461 × 1015 | m |
| Planck constant | 6.62607015 × 10−34 | J·s |
| Mass of an electron | 9.109 × 10−31 | kg |
Need more precision rules? Use the significant figures calculator.
Benefits of using scientific notation
Scientific notation makes extreme numbers easier to read, compare and calculate with.
Read huge numbers fast. 6.02 × 1023 is far clearer than 24 written digits.
Compare sizes at a glance. The exponent shows the order of magnitude instantly.
Show precision clearly. 1.20 × 103 tells readers there are three significant figures.
Avoid copying errors. Fewer zeros mean fewer mistakes in homework and lab reports.
Match your calculator. Learn to read the E notation that calculators and spreadsheets display.
Work with SI units. Engineering notation lines up with prefixes like kilo, mega and micro.
Scientific notation calculator FAQs
Quick answers for students, teachers and anyone working with very big or very small numbers.
Scientific notation writes a number as a coefficient from 1 to just under 10, multiplied by a power of 10. For example, 45,600 becomes 4.56 × 104, and 0.00032 becomes 3.2 × 10−4.
Move the decimal point until one non-zero digit sits to its left, and count how many places you moved it. That count is the exponent. It is positive if you moved the point left and negative if you moved it right.
Move the decimal point four places to the right to get 5. Because you moved it right, the exponent is negative, so 0.0005 = 5 × 10−4.
E notation is how calculators, spreadsheets and programming languages show scientific notation. The letter E means times 10 to the power of, so 6.02E23 equals 6.02 × 1023.
In scientific notation the coefficient runs from 1 to just under 10. In engineering notation the exponent is always a multiple of 3, so the coefficient runs from 1 to just under 1,000. This lines up with SI prefixes such as kilo, mega and micro.
Multiply the coefficients and add the exponents. For example, (3 × 104) × (2 × 105) = 6 × 109. If the new coefficient is 10 or more, move the decimal point one place left and add 1 to the exponent.
First rewrite both numbers with the same exponent. Then add the coefficients and keep that exponent. For example, 3.2 × 105 + 4.5 × 104 = 3.2 × 105 + 0.45 × 105 = 3.65 × 105.
Yes, for addition, subtraction, multiplication and whole-number powers. It uses exact decimal arithmetic instead of floating-point numbers, so 0.1 + 0.2 gives exactly 0.3. Division is precise to 30 significant figures.
Convert and calculate with confidence
From homework to lab reports, this scientific notation calculator gives exact answers in every format, with the working shown so you can learn the method too.
Division results are rounded to 30 significant figures. Very large standard-form numbers (over 400 digits) are shown in scientific notation only.