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Scientific Notation Converter

Converters · Added

Type a number in any form — 0.000045, 4.5e-5 or 4.5 × 10⁻⁵ — and get all of them back, along with the significant figures it was written to and the SI prefix its engineering form corresponds to.

Plain, scientific or engineering. 4.5e-5, 4.5E-5 and 4.5 × 10^-5 are all accepted.

Leave on 'as written' to keep the precision of what you typed.

Try:

How to use the scientific notation converter

  1. 1Enter the number in whichever notation you have it.
  2. 2Leave the precision on 'as written' to keep what you typed, or pick a number of significant figures to round to.
  3. 3Copy whichever form you need — each has its own copy button.
  4. 4Check the significant figures row if the number came from a measurement.

Examples

A capacitor value

Input
0.000045
Result
Scientific 4.5 × 10⁻⁵ · Engineering 45 × 10⁻⁶ · SI prefix µ (micro)

Ambiguous trailing zeros

Input
4500
Result
Read as two significant figures, with a note explaining why that is a convention rather than a fact

About the scientific notation converter

Significant figures are a claim about a measurement

Writing 2.50 metres rather than 2.5 says the measurement was good to the centimetre. Writing 2.500 says it was good to the millimetre. The digits are not decoration — they are the statement of how much you know, and adding digits you did not measure is a claim you cannot support.

This is why calculation rules exist for them. Multiplying a three-figure value by a five-figure one gives a three-figure answer, because the result cannot be more certain than the least certain input. Carrying the full float through and rounding at the end is right; rounding intermediate values is what accumulates error.

Reading E notation without misreading it

A calculator that shows 4.5E-5 means 4.5 × 10⁻⁵. The E stands for exponent and has nothing to do with Euler's number, which is the misreading that turns up most often.

The other trap is spreadsheet software, which switches into E notation on its own once a number is long enough, and which will happily convert a long identifier into a float on paste. A part number of 1E5 becomes 100000 and the original is gone. Where a value is an identifier rather than a quantity, it belongs in a text column.

Frequently asked questions

What is the difference between scientific and engineering notation?
Scientific notation puts exactly one digit before the decimal point, so the mantissa is always between 1 and 10. Engineering notation instead forces the exponent to a multiple of three, which lets the mantissa run from 1 to 1000. The point of the second is that the exponents then line up with the SI prefixes — 45 × 10⁻⁶ farads is 45 microfarads, which is how the component is actually labelled.
Why are the trailing zeros in a number like 4500 ambiguous?
Because the notation does not record whether they were measured or are placeholders. A count of exactly 4500 items has four significant figures; a crowd estimated at 4500 has two. Written in scientific notation the ambiguity vanishes — 4.5 × 10³ is two figures and 4.500 × 10³ is four — which is one of the better arguments for the notation.
How are significant figures counted?
Leading zeros never count, digits between non-zero digits always count, and trailing zeros count when there is a decimal point anywhere in the number. So 0.00230 has three, 1002 has four, and 1200 has two by convention with the caveat above.
Is there a limit to the numbers it handles?
The arithmetic runs in double-precision floating point, so magnitudes beyond about 10³⁰⁸ overflow and anything below about 10⁻³²⁴ underflows to zero. Both are refused with an explanation instead of returning infinity or zero, since either would look like a real answer.

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