Scientific
Scientific Notation Calculator: Convert And Calculate In A × 10ⁿ Form
Last updated: October 2026
Written by Jessica Hill
A scientific notation calculator writes a number as a × 10ⁿ, where a is at least 1 and less than 10, and n is a whole number. For example, 422,000 = 4.22 × 10⁵ and 0.00057 = 5.7 × 10⁻⁴. A positive exponent means a large number. A negative exponent means a number smaller than 1.
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Scientific notation keeps huge and tiny numbers short and easy to compare.
What Scientific Notation Is
Scientific notation is a short way to write any number as a coefficient times a power of 10. The coefficient must be at least 1 and less than 10. The exponent tells you how many places to move the decimal point.
| Standard form | Scientific notation | Exponent meaning |
|---|---|---|
| 422,000 | 4.22 × 10⁵ | Move the decimal 5 places right |
| 0.0082 | 8.2 × 10⁻³ | Move 3 places left |
| 0.00057 | 5.7 × 10⁻⁴ | Move 4 places left |
For example, the speed of light, 299,792,458 m/s, rounds to 3.00 × 10⁸ m/s.
How To Use The Scientific Notation Calculator
Use the Convert tab to see any number in all four forms, the Calculate tab for step-by-step arithmetic, and the Significant Figures tab to round your answer correctly.
How To Convert To Scientific Notation
Move the decimal point until one non-zero digit is left of it. The number of moves is the exponent: positive for numbers 10 or more, negative for numbers less than 1.
Large number: 422,000
- Place the decimal after the first digit: 4.22000.
- You moved it 5 places left.
- Drop trailing zeros: 4.22 × 10⁵.
Small number: 0.00057
- Move the decimal right until it sits after the 5: 5.7.
- You moved it 4 places right.
- So the exponent is negative: 5.7 × 10⁻⁴.
To go back to standard form, reverse the move. For 3.08 × 10⁻³, move the decimal 3 places left and fill with zeros: 0.00308.
E-Notation And Engineering Notation
Calculators and computers show the same value in different styles.
| Format | Rule | 456,000,000 |
|---|---|---|
| Scientific notation | 1 ≤ a < 10 | 4.56 × 10⁸ |
| E-notation | "× 10^" replaced by e or E | 4.56e8 |
| Engineering notation | Exponent is a multiple of 3 | 456 × 10⁶ |
Engineering notation matches metric prefixes. An exponent of 3 is kilo, 6 is mega, 9 is giga, −3 is milli and −6 is micro.
Calculating In Scientific Notation
After any operation, check that the coefficient is still between 1 and 10.
Multiplying And Dividing
To multiply, multiply the coefficients and add the exponents. To divide, divide the coefficients and subtract the exponents.
- (3 × 10⁴)(2 × 10⁵) = 6 × 10⁹
- (8.4 × 10⁶) ÷ (2.1 × 10²) = 4 × 10⁴
- (9.6 × 10⁻⁴) ÷ (3.2 × 10⁻⁷) = 3 × 10³, because −4 − (−7) = 3
When the coefficient goes out of range, normalize it. (5 × 10³)(4 × 10²) = 20 × 10⁵. Since 20 is more than 10, write it as 2.0 × 10¹ × 10⁵ = 2 × 10⁶.
For powers, raise the coefficient and multiply the exponent: (2 × 10³)² = 4 × 10⁶.
Adding And Subtracting
To add or subtract, the exponents must match first. Rewrite the smaller number so it has the same exponent as the larger one, then add or subtract the coefficients.
Solve 5.3 × 10⁵ + 3.8 × 10⁴:
- Rewrite 3.8 × 10⁴ as 0.38 × 10⁵.
- Add the coefficients: 5.3 + 0.38 = 5.68.
- Answer: 5.68 × 10⁵.
Subtraction works the same way: 7.5 × 10⁸ − 2.5 × 10⁷ = 7.5 × 10⁸ − 0.25 × 10⁸ = 7.25 × 10⁸.
Scientific Notation And Significant Figures
In scientific notation, every digit in the coefficient is significant. That makes it the clearest way to show precision.
The number 0.005600 has 4 significant figures, since leading zeros do not count but trailing zeros after a decimal do. In scientific notation, it is 5.600 × 10⁻³, and the 4 sig figs are easy to see.
It also fixes ambiguous numbers like 1,500: 1.5 × 10³ has 2 sig figs, while 1.500 × 10³ has 4.
Some constants are now defined exactly. Since the SI units were redefined on May 20, 2019, the Avogadro constant has been fixed at exactly 6.02214076 × 10²³ per mole, as Physics World reported on the SI redefinition.
Entering Scientific Notation On A Calculator
Most scientific calculators have a key labeled EE, EXP or ×10ˣ. Use it instead of typing × 10 ^ by hand.
To enter 5.7 × 10⁻⁴, type 5.7, press EE (or EXP), then type −4. Do not also type × 10, or the answer will be 10 times too big. To see every answer in scientific notation, switch the calculator to SCI mode in its setup menu. The scientific calculator on this site accepts E-notation directly, like 5.7e-4.
Common Scientific Notation Mistakes
- Coefficient out of range. 45 × 10³ is not in scientific notation. Write 4.5 × 10⁴.
- Wrong exponent sign. 0.0082 is 8.2 × 10⁻³, not 8.2 × 10³.
- Adding exponents when adding numbers. Exponents only add when you multiply. For addition, match the exponents first.
Summary
- Scientific notation is a × 10ⁿ, with 1 ≤ a < 10.
- Count decimal moves to get the exponent: positive for large numbers, negative for small ones.
- Multiply or divide coefficients and add or subtract exponents. For addition, match exponents first.
Next step: enter your number in the scientific notation calculator at the top of this page. For percentages of big numbers, try the percentage calculator, or see every tool on the Calc Solver homepage.
Frequently Asked Questions
What is 10 in scientific notation?
10 in scientific notation is 1 × 10¹. The coefficient is 1 and the decimal moves one place. In the same way, 100 is 1 × 10², 1,000 is 1 × 10³ and 1,000,000 is 1 × 10⁶. For powers of ten, the exponent is simply the number of zeros after the 1.
What is 0.0001 in scientific notation?
0.0001 in scientific notation is 1 × 10⁻⁴. Move the decimal point 4 places to the right to get 1, so the exponent is −4. The same pattern works for all decimal powers of ten: 0.1 is 1 × 10⁻¹, 0.01 is 1 × 10⁻² and 0.001 is 1 × 10⁻³.
Is standard form the same as scientific notation?
It depends on where you learned math. In the UK and some other countries, "standard form" means scientific notation, like 4.22 × 10⁵. In the United States, "standard form" usually means the regular way of writing a number, like 422,000. Check your textbook if a question asks for "standard form."
Can the coefficient be 10 or more?
No. In proper scientific notation, the coefficient must be at least 1 and less than 10. A number like 12 × 10⁴ should be rewritten as 1.2 × 10⁵. Engineering notation allows coefficients from 1 up to 999, because its exponents must be multiples of 3, but that is a different format.
How do I write negative numbers in scientific notation?
Put the negative sign in front of the coefficient and convert as usual. For example, −4,500 becomes −4.5 × 10³, and −0.00031 becomes −3.1 × 10⁻⁴. The sign of the exponent still depends only on the size of the number, not on whether the number itself is negative.
Try it with your own numbers
The calculator at the top of this page uses the same formulas as the examples.