Maths / Notation
Scientific Notation Converter
Convert numbers to scientific notation (a × 10ⁿ), engineering notation, and E notation, and back to standard form.
Scientific Notation Converter: In scientific notation, a number is written as a × 10ⁿ with one non-zero digit before the decimal point: 45,600 = 4.56 × 10⁴ and 0.000456 = 4.56 × 10⁻⁴. Engineering notation chooses the exponent as a multiple of 3, so it lines up with unit prefixes: 45.6 × 10³ is 45.6 thousand. The conversion works on the digits as typed, so long numbers keep every digit. Runs 100% locally in your browser with zero server file uploads.
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Scientific notation writes a number as a × 10ⁿ with 1 ≤ |a| < 10. Engineering notation keeps n a multiple of 3, matching the prefixes kilo, mega, milli, and micro.
Examples from science
Avogadro's number is 6.022 × 10²³; the speed of light 2.998 × 10⁸ m/s; an electron's charge 1.602 × 10⁻¹⁹ C; the width of a human hair about 7 × 10⁻⁵ m. Written out, these would need dozens of zeros.
To count the digits that matter, use the significant figures calculator; for powers and logarithms, the log calculator.
Multiplying and dividing
Multiply the a parts and add the exponents: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷. Divide the a parts and subtract the exponents. Then shift the decimal point so that a is again between 1 and 10.
How to use it
- Type a number in standard form, such as 0.000456, or in E notation, such as 6.02e23.
- Read it in scientific and engineering notation.
- Copy the E form for spreadsheets and calculators.
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Frequently asked questions
What does E mean in 6.02E23?
E stands for 'times ten to the power': 6.02E23 = 6.02 × 10²³. Calculators and spreadsheets use it for very large and small numbers.
When is the exponent negative?
For numbers smaller than 1: the exponent counts how many places the decimal point moves to the right to reach the first non-zero digit.
What are significant figures in scientific notation?
Every digit of a is significant, so 4.50 × 10³ shows three significant figures where 4500 is ambiguous.
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