One field, four notations detected
There is nothing to choose before typing. The parser works out whether it received a decimal, a power of ten, an E-notation value, or an already-engineering-shaped number, and says which it found.
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Scientific Notation Converter
Read any number back in all four notations at once: written out in full, normalised to one digit, in E-notation, and in engineering form with the SI prefix that matches.
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0.00000123 is 1.23 times ten to the power minus 6 in scientific notation, 1.23e-6 in E-notation, and 1.23 times ten to the power minus 6 in engineering notation, or 1.23 micro.
Notation desk
Type the number however you have it
A decimal, an e, a caret, or a superscript: the form is detected from what you type, and the other four are written out underneath.
Read as plain decimal3 significant figuresOrder of magnitude 10⁻⁶
Rounds the mantissa half away from zero and rewrites all five forms.
Joins the prefix: 1.23 µF.
Load a constant
Normalised scientific notation
1.23×10−6
0.00000123 read as plain decimal, then normalised to one digit before the point.
Precision as enteredmicro range
Significant figures
3
Order of magnitude
10⁻⁶
Decimal places
8
Digits written out
9
Engineering exponent
10⁻⁶
SI prefix
micro (µ)
Every form at once
The same number, written five ways
Each row copies as plain text. The decimal expansion is built character by character, so nothing is lost to floating point.
Plain decimal
Every digit written out, with the point where it belongs.
0.00000123
Scientific notation
Normalised: exactly one non-zero digit in front of the point.
1.23×10−6
Also written 1.23e-6
E-notation
What calculators, spreadsheets, and code accept as typed input.
1.23e-6
Paste straight into a cell or a source file.
Engineering notation
Exponent forced onto a multiple of three; mantissa runs 1 to 999.
1.23×10−6
Identical to the scientific form here; the exponent was already a multiple of three.
SI prefix form
The engineering exponent said out loud, ready to sit in front of a unit.
1.23 µ
micro · symbol µ · 10⁻⁶
Prefix reference
Every SI prefix, and something that size
The twenty engineering prefixes step in thousands. Hecto, deca, deci, and centi do not, which is why they never appear in engineering notation.
| Prefix | Symbol | Power of ten | Something that size |
|---|---|---|---|
| quetta | Q | 1030 | Adopted in 2022, ahead of the data volumes that will need it: the Sun weighs about 2,000 quettagrams. |
| ronna | R | 1027 | Earth weighs about 6 ronnagrams, 5.97 × 10²⁴ kg written the short way. |
| yotta | Y | 1024 | A mole of anything is 0.602 yotta-particles: Avogadro's 6.022 × 10²³. |
| zetta | Z | 1021 | The oceans hold roughly 1.3 zettalitres of water. |
| exa | E | 1018 | One exametre is about 106 light-years. |
| peta | P | 1015 | A petabyte is a million gigabytes; research archives are sized in them. |
| tera | T | 1012 | A terabyte drive, or the terahertz band just above microwaves. |
| giga | G | 109 | A 3 GHz processor ticks three billion times a second. |
| mega | M | 106 | A megapixel is a million pixels; a megawatt is a million watts. |
| kilo | k | 103 | A kilometre is a thousand metres. Note the lower-case k. |
| hectoNot engineering | h | 102 | Air pressure on a weather map: 1013 hPa at sea level. |
| decaNot engineering | da | 101 | Rare outside textbooks: a decametre is ten metres. |
| deciNot engineering | d | 10−1 | A decilitre in a recipe, and the deci hiding inside the decibel. |
| centiNot engineering | c | 10−2 | A centimetre is a hundredth of a metre. |
| milli | m | 10−3 | A millimetre is about the width of a grain of coarse sand. |
| microIn use | µ | 10−6 | A human hair is roughly 70 micrometres across. |
| nano | n | 10−9 | Visible light runs from about 380 to 700 nanometres. |
| pico | p | 10−12 | Light crosses a third of a millimetre in one picosecond. |
| femto | f | 10−15 | An atomic nucleus measures a few femtometres. |
| atto | a | 10−18 | Attosecond laser pulses track electrons, the 2023 physics Nobel. |
| zepto | z | 10−21 | Light needs about 247 zeptoseconds to cross a hydrogen molecule. |
| yocto | y | 10−24 | A proton weighs roughly 1.67 yoctograms. |
| ronto | r | 10−27 | New in 2022: an electron weighs about 0.91 rontograms. |
| quecto | q | 10−30 | Also new in 2022, and about a thousandth of an electron's mass. |
Normalised means one digit
Scientific notation allows exactly one non-zero digit before the point, so 0.5 × 10⁻⁵ and 50 × 10⁻⁷ are the same quantity written badly. Both normalise to 5 × 10⁻⁶.
Engineering keeps the exponent divisible by three
That is what lets the exponent be spoken as a prefix. 1.23 × 10⁻⁶ and 123 × 10⁻⁹ are equal; only the second matches nano, and only the first matches micro.
A negative exponent is a small number
10⁻⁶ means divide by a million, not multiply. Count the exponent's places to the left of the first digit: 10⁻⁶ puts five zeros between the point and the 1.23.
Everything on this page is decimal-point arithmetic on the digits you typed, done in your browser. Nothing is uploaded, none of your digits pass through a floating-point number, and the expansion of a large exponent is exact rather than rounded to seventeen digits. Powers beyond 10^9999 are refused because writing them out would produce a page nobody can read.
Continue the workflow
Before the number, and after it.
Advanced Scientific Calculator
Do the logarithms, powers, and trigonometry that produced the number before you write it up.
Unit Converter
Change the unit itself (metres to miles, joules to calories) once the magnitude is settled.
Average Calculator
Reduce a column of measurements to a mean, with the precision control a lab write-up needs.
How it works
One number, written whichever way the page asks for.
Notation is presentation, not arithmetic: 0.00000123, 1.23e-6, 1.23 × 10⁻⁶, and 1.23 micro are one quantity in four costumes. This page reads whichever costume you arrive in, keeps the digits intact rather than rounding them into a floating-point number, and hands back the rest.
- 01
Type the number in the form you already have
A decimal such as 0.00000123, a calculator readout such as 1.23E-6, or the typeset 1.23 × 10⁻⁶ all work. Superscripts, unicode multiplication signs, and grouped digits are understood, and the form you used is named back to you.
- 02
Set the significant figures the answer should keep
Leave it on “as entered” to preserve every digit you supplied, or pick a count from 1 to 15. The mantissa rounds half away from zero and short values are padded, so four significant figures on 1.5 gives 1.500.
- 03
Copy the notation your work asks for
Each of the five rows has its own copy button: the written-out decimal for a form field, the typeset power of ten for a report, E-notation for a spreadsheet, and the prefix form for a component label.
Built for homework and lab reports
Exact digits, honest significant figures, real SI prefixes.
Expansion done digit by digit
The decimal form is built by walking the decimal point through the digit string, never by passing the value through a floating-point number. 1.23 × 10³⁰ expands to a clean 1 followed by 2, 3, and twenty-eight zeros.
Long tails survive the trip
A twenty-digit mantissa keeps all twenty digits. Nothing is quietly truncated at the seventeenth, which is where a double-precision number gives up and starts inventing endings.
Significant figures applied everywhere at once
Choosing three significant figures rewrites the decimal, the scientific form, the E-notation, the engineering form, and the prefix form together, so the whole answer states the same precision.
Engineering notation with its prefix
The exponent is pushed to the nearest multiple of three below the value and matched against the SI table, so 1.23 × 10⁻⁶ also appears as 1.23 µ, and as 1.23 µF once you name the unit.
Constants a click away
The speed of light, Avogadro's number, the Planck and Boltzmann constants, the elementary charge, the electron mass, the Bohr radius, and the astronomical unit load straight into the field with their units attached.
Notation questions
Exponents, significant figures, and where the prefixes come from.
How do I put a number into scientific notation?+
Move the decimal point until exactly one non-zero digit sits in front of it, then count how far it travelled. Each place to the left adds one to the exponent, each place to the right subtracts one. For 0.00000123 the point moves six places right, giving 1.23 × 10⁻⁶; for 149,600,000 it moves eight places left, giving 1.496 × 10⁸. Zero is the exception: it has no leading non-zero digit, so it is simply written 0.
What is the difference between scientific and engineering notation?+
Scientific notation insists on one digit before the point and lets the exponent be anything. Engineering notation gives up that rule and insists instead that the exponent be a multiple of three, which leaves a mantissa somewhere between 1 and 999. The same quantity is 1.23 × 10⁻⁷ scientifically and 123 × 10⁻⁹ in engineering form. Engineers prefer the second because every multiple of three has a spoken name: 123 nanofarads is something you can order, ask for, and read off a reel.
Why does my calculator show 1.23E-6 instead of 1.23 × 10⁻⁶?+
Because a seven-segment display and a keyboard have no superscripts. E-notation is a typing convention, not a different quantity: the E means “times ten to the power of”, so 1.23E-6, 1.23e-6, and 1.23 × 10⁻⁶ are the same number. Spreadsheets, programming languages, and lab instruments all accept the E form, which is why it is worth copying from here rather than retyping.
How do I read a negative exponent?+
A negative exponent divides rather than multiplies. 10⁻⁶ means one millionth, so 1.23 × 10⁻⁶ is 1.23 divided by a million. When writing it out, the exponent tells you how many places the point moves left: six places from 1.23 lands on 0.00000123, with five zeros between the point and the 1. A common slip is counting the zeros instead of the places; there is always one fewer zero than the exponent when the mantissa is at least 1.
How many significant figures does the answer keep?+
Whatever the input claimed, unless you say otherwise. Digits are counted from the first non-zero one, so 0.00500 carries three significant figures and 1.496 × 10⁸ carries four. Trailing zeros in a plain whole number are treated as place-holders rather than measurements, which is why 149600000 is read as four significant figures; write it as 1.49600000 × 10⁸ if all nine really were measured.
Can rounding change the power of ten?+
Yes, and that is the case worth watching. Rounding 9.99 × 10² to two significant figures gives 10 × 10², which is not normalised, so it is rewritten as 1.0 × 10³; the exponent climbed by one. The converter handles the carry itself, so the mantissa always comes back with a single digit before the point no matter how many nines were rounded away.
How does an exponent become a prefix like micro or nano?+
By matching the engineering exponent against the SI prefix table: 10⁻³ is milli, 10⁻⁶ micro, 10⁻⁹ nano, 10³ kilo, 10⁶ mega, 10⁹ giga, and so on out to quetta and quecto at 10³⁰ and 10⁻³⁰. Only multiples of three have prefixes in this range, which is exactly why engineering notation exists. Hecto, deca, deci, and centi sit on 10², 10¹, 10⁻¹, and 10⁻², so they never turn up in engineering notation even though centimetres are everywhere.
Is the conversion exact for very large or very precise numbers?+
Yes. Every step is string arithmetic on the digits you typed, so a thirty-place expansion is written out in full rather than approximated. Spreadsheets and most online converters route the value through a 64-bit float first, which is why a pasted twenty-digit mantissa can come back with an unfamiliar tail around the seventeenth digit. Nothing here ever becomes a float, and the only limit is a refusal to expand exponents beyond 10⁹⁹⁹⁹.
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