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Scientific Notation Converter

How do I write scientific notation?

How it is calculated

Scientific notation writes a number as m × 10e with the mantissa m at least 1 and below 10 in size. The exponent is e = floor(log10|x|) and the mantissa is m = x / 10e. The tool rounds the mantissa to two decimals, so digits beyond that are lost in the display. The rounding happens first, so 9.999 becomes 1.00 × 10^1, never 10.00. It also prints e-notation (4.52e6), the form calculators, spreadsheets and code accept; that field always uses a decimal point, whatever language the page is in. Zero is returned as 0. Negative numbers keep their sign on the mantissa, and numbers below 1 get a negative exponent.

Worked example

Write 4,523,000. It lies between 106 and 107, so the exponent is 6. The mantissa is 4,523,000 / 1,000,000 = 4.523, rounded to 4.52. The result is 4.52 × 10^6, and the e-notation is 4.52e6. Rounding means 4.52 × 106 is 4,520,000, slightly off the original.

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Common mistakes

  • Moving the decimal point the wrong number of places, so the mantissa ends up outside 1 to 10.
  • Getting the exponent sign wrong for small numbers: 0.00045 is 4.5 × 10−4, not 104.
  • Treating the rounded mantissa as exact; only two decimals are kept.
  • Reading e in e-notation as Euler's number; it means "times ten to the power".

About this calculator

This converter rewrites a number into scientific notation (a × 10ⁿ, where |a| is between 1 and 10) as well as E-notation (the calculator-and-programming-friendly form like 6.02e23), which is the format many calculators, spreadsheets and programming languages default to once a number gets too large or too small to display comfortably in full.

Scientists and engineers use scientific notation to keep extremely large numbers (like Avogadro's number or a star's mass) and extremely small ones (like an atom's radius) readable and easy to compare by exponent alone, and students use this converter to check homework or to translate between the two notations when a textbook uses one form and a calculator or spreadsheet displays the other.

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Comments (1)

  • Editorial team

    Only two decimals of the mantissa survive, so 6.02214 × 10^23 comes out as 6.02e23. That is fine for reading a magnitude but not for further arithmetic, so keep your original figure for any follow-on calculation. The e-notation line is written with a decimal point, which is the form most programming languages expect. Paste a number whose result looks off and tell us what you expected.

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