Scientific Notation Calculator
Convert between decimal, scientific, and engineering notation: done on the digits, so nothing is lost to rounding.
Details
Plain or e-notation: 0.00045, 123456, 4.5e-4.
Scientific notation
4.5 × 10⁻⁴
The number part
4.5
The power of 10
-4
Significant digits
2
Engineering exponent
-6
This converts between ordinary numbers and scientific notation in both directions. Enter a full number like 0.00045 to get 4.5 × 10⁻⁴, or enter a coefficient and exponent to get the number written out.
It also returns the E notation a calculator screen would show, and the number of significant figures.
What is scientific notation?
Scientific notation is a short way of writing very large or very small numbers, so you do not have to count zeros.
Every number is written as one digit, a decimal point, then a power of ten. So 0.00045 becomes 4.5 × 10⁻⁴, and 300,000,000 becomes 3 × 10⁸.
The power of ten just records how far the decimal point moved, which is the same idea the exponent calculator handles on its own. Nothing about the number's value changes, only how it is written down.
A negative exponent means a small number, not a negative one. 4.5 × 10⁻⁴ is 0.00045, which is positive. The minus refers to the direction the decimal point moved, not the sign of the value.
What to enter
- Convert
- Choose which way you are going: a full number into scientific notation, or scientific notation back into a full number.
- Number
- The number written out in full, like 0.00045 or 93000000.
- Coefficient (a)
- The front part. To be proper scientific notation it must be at least 1 and less than 10.
- Exponent (n)
- The power of ten. Positive for big numbers, negative for small ones.
Related ways of writing the same thing
- Scientific notation
- One digit before the point, so 4.5 × 10⁻⁴. The standard form in science and maths.
- E notation
- What calculators and spreadsheets show when the screen is too narrow: 4.5E-4 means exactly 4.5 × 10⁻⁴. The E stands for exponent, not the number e.
- Engineering notation
- Like scientific notation, but the exponent is always a multiple of 3 so it lines up with kilo, mega, milli and micro. 45,000 becomes 45 × 10³ rather than 4.5 × 10⁴.
- Standard form
- The same thing as scientific notation. British and many international syllabuses use this name instead.
What this assumes
Proper scientific notation keeps the coefficient at 1 or above and below 10. 45 × 10³ is a valid number but is not correctly formatted.
How to calculate scientific notation
Move the decimal point until one non-zero digit sits in front of it, then count how far you moved.
- a
- The coefficient: one digit, then the decimals
- n
- How many places the point moved, and which way
Move the point. Slide it until exactly one non-zero digit is on the left.
Count the moves. That number is your exponent.
Get the sign right. Moving left on a big number gives a positive exponent. Moving right on a small number gives a negative one.
Sanity check. Big numbers get positive powers, small numbers get negative ones. If your answer breaks that, the sign is flipped.
See a worked example: writing 0.00045 in scientific notation
- Number
- 0.00045
Start at 0.00045 and move the decimal point right until one non-zero digit is in front: 4.5
Count the moves: 0.0045, 0.045, 0.45, 4.5. That is four places.
The number is small and the point moved right, so the exponent is negative.
That gives 4.5 × 10⁻⁴. A calculator may display this as 4.5E-4.
4.5 × 10⁻⁴
Frequently asked questions
No, and this is the mistake nearly everyone makes first. 4.5 × 10⁻⁴ = 0.00045, which is positive.
A negative exponent means the number is small, less than one. The value is only negative if the coefficient itself carries a minus sign, as in −4.5 × 10⁻⁴.
It is shorthand for '× 10 to the power of'. 4.5E-4 means 4.5 × 10⁻⁴, and 2.6E8 means 2.6 × 10⁸.
Calculators use it because superscripts are hard to display. The E has nothing to do with Euler's number e, which is a completely different thing.
Scientific notation always puts exactly one digit before the point. Engineering notation instead forces the exponent to be a multiple of 3.
That is because 3, 6 and 9 line up with the prefixes people actually use: kilo, mega, giga, milli, micro. So 45,000 is 4.5 × 10⁴ scientifically, but 45 × 10³ in engineering, which reads directly as 45 kilo-anything.
Yes. They are two names for the same format, and both mean a × 10ⁿ with the coefficient between 1 and 10.
'Standard form' is the usual term in British and many international syllabuses, while 'scientific notation' is more common in the US.
Multiply the coefficients, then add the exponents. For (3 × 10⁴) × (2 × 10³) that gives 6 × 10⁷.
For division, divide the coefficients and subtract the exponents. If the coefficient ends up outside 1 to 10, shift the point and adjust the exponent to tidy it up.
Problems people actually run into
Getting the sign of the exponent backwards
Writing 0.00045 as 4.5 × 10⁴ instead of 10⁻⁴ turns a tiny number into 45,000, an error of a hundred million times.
The check that always works: if the original number is smaller than 1, the exponent must be negative. If it is bigger than 10, the exponent must be positive.
Leaving the coefficient outside 1 to 10
45 × 10³ has the right value but is not correctly written, and in an exam it usually costs the mark.
Shift the point one more place and add one to the exponent: 45 × 10³ becomes 4.5 × 10⁴. Every move left adds one, every move right subtracts one.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 3, 2026