Scientific Notation Converter: E and Engineering
Convert numbers to and from scientific notation, E notation and engineering notation with exact significant-figure rounding, or write them as powers of two with the binary significand and hex float. Free and private in your browser.
- Scientific notation
- 1.23456 × 10^5
- E notation
- 1.23456E5
- Engineering notation
- 123.456 × 10^3
- Decimal
- 123456
- Significant figures
- 6
About the Scientific Notation Converter
The Scientific Notation Converter rewrites a number in the forms used in science, engineering and programming. In the Powers of ten view it shows scientific notation (a × 10ⁿ, where a is at least 1 and below 10), E notation as calculators and spreadsheets print it, engineering notation (an exponent that is a multiple of 3) and the ordinary decimal. In the Powers of two view it writes the number as a × 2ⁿ, shows its binary exponent, its 53-bit binary significand, the C hexadecimal float, and the powers of two on either side of it.
You can type a plain decimal such as 0.00015, grouped thousands such as 1,234,500, E notation such as 6.02e23 or a power of ten such as 1.5 × 10^-7, so it converts both to and from scientific notation. All arithmetic is exact on decimal digits, so you never see floating-point noise such as 0.30000000000000004. Everything runs in your browser and nothing is sent anywhere.
How to use it
Steps
- Choose Powers of ten or Powers of two.
- Type the number. Commas, spaces,
eorE,× 10^and superscript exponents such as 10⁻³ are all understood. - Optionally enter a number of significant figures. Leave it empty to keep the figures as typed.
- Each result has its own Copy button.
Limits
Up to 1,000 digits and powers of ten from 10^−1000 to 10^1000 are accepted, and from 1 to 1,000 significant figures.
The notations
Scientific
The number is written as one non-zero digit, a decimal point, the remaining figures and a power of ten: 123,456 = 1.23456 × 10^5 and 0.00042 = 4.2 × 10^-4. The exponent is the number of places the decimal point moves.
E notation
The same number with "× 10^" replaced by the letter E, so 1.23456 × 10^5 becomes 1.23456E5 and 4.2 × 10^-4 becomes 4.2E-4. Spreadsheets, calculators and most programming languages read and print this form.
Engineering
The exponent is a multiple of 3, so the mantissa lies from 1 to 999 and lines up with the SI prefixes kilo, mega, milli and micro: 123,456 = 123.456 × 10^3 and 0.00012 = 120 × 10^-6.
Significant figures
Digits typed after a decimal point count as significant, so 1.200 keeps four figures, 1.200 × 10^0. Trailing zeros of a whole number without a point, such as 1200, are treated as placeholders, so 1200 becomes 1.2 × 10^3. To keep them, type 1200. or choose 4 significant figures. Rounding is to the nearest value, with halves rounded away from zero: 9.996 to three figures is 1.00 × 10^1, and −2.5 to one figure is −3 × 10^0.
Powers of two
Every non-zero number lies between two neighbouring powers of two: at least 2ⁿ and below 2ⁿ⁺¹. It can therefore be written as a × 2ⁿ, where a is at least 1 and below 2. Because 1/2 = 0.5, that significand is always an exact, finite decimal: 12 = 1.5 × 2^3 and 0.1 = 1.6 × 2^-4.
The binary significand and the hexadecimal float show what a double-precision (IEEE 754) number keeps: a leading 1 and 52 more bits, rounded to the nearest value with ties to even. 12 is exactly 0x1.8p+3, while 0.1 has no finite binary form and is stored as 0x1.999999999999ap-4, which the page labels as rounded. The nearest power of two compares |x| with the two neighbours; 100 lies between 64 and 128 and is nearer 128, while 12 is exactly half-way between 8 and 16.
Privacy
The conversion is done by code on this page. Nothing is uploaded, and nothing is kept after you close the tab.
Related tools
To raise numbers to powers or take logarithms, use the Exponent Calculator. To write integers in binary, octal or hexadecimal, use the Number Base Converter. To break a whole number into prime factors, use the Prime Factorization Calculator.
Open-source credits
- The converter is written for this site and uses no third-party library. Decimal values are held as digit strings and the browser's built-in
BigInt, so no binary floating-point step is involved. - The binary significand follows the binary64 format and round-to-nearest-even rule of IEEE 754-2019, and the hexadecimal float follows the
%aconversion of ISO/IEC 9899 (C99 and later); the tests check 0.1 against the published%aoutput 0x1.999999999999ap-4. - Engineering notation follows the SI prefix steps of the International Bureau of Weights and Measures, The International System of Units, 9th edition (2019).
Frequently asked questions
What is the difference between scientific and engineering notation?
Scientific notation keeps one digit before the point, as in 1.23456 × 10^5. Engineering notation uses only exponents that are multiples of three, as in 123.456 × 10^3, so values line up with kilo, mega and milli.
What does E mean in a number like 6.02E23?
E stands for times ten to the power of, so 6.02E23 is 6.02 × 10^23. Calculators, spreadsheets and programming languages use the letter because a superscript is hard to type and print.
How are significant figures rounded?
The number is rounded to the nearest value with the chosen figures, and an exact half is rounded away from zero. Asking for more figures than were typed pads the mantissa with zeros, so 1.2 to four figures reads 1.200.
Why is 0.1 marked as rounded in the powers of two view?
One tenth has no finite binary expansion, just as one third has none in decimal. A double keeps 53 bits, so 0.1 is stored as 0x1.999999999999ap-4, a value very slightly above 0.1.
Can I convert from scientific notation back to a normal number?
Yes. Type the value in any form, such as 1.5e-7 or 1.5 × 10^-7, and the Decimal row shows it written out in full, here 0.00000015, with every digit exact.