Scientific and Engineering Notation Converter with SI Prefixes
Heading to the field? Install this site from your browser menu and this tool works with no signal. See how
Scientific and Engineering Notation Converter
Turns any number into scientific notation, engineering notation and an SI prefix in one pass. Engineering notation keeps the exponent a multiple of three, which is why it maps straight onto kilo, mega, milli and micro.
Scientific notation puts the mantissa between 1 and 10. Engineering notation lets it run from 1 to 999 so the exponent lands on a power of a thousand. That is the whole trick: 4.7 x 10^-4 A reads as maths, 470 x 10^-6 A reads as 470 microamps.
How to use this tool
Type a number in plain or e notation, optionally add a unit symbol, and the tool returns it four ways: plain decimal, scientific notation, engineering notation and, where one exists, the SI prefix form. The big result is the engineering form because that is usually the one people actually want.
Scientific against engineering notation
Scientific notation forces the mantissa between 1 and 10, so 0.00047 becomes 4.7 x 10^-4. Mathematically tidy, and unreadable in a workshop. Engineering notation instead forces the exponent to a multiple of three and lets the mantissa run from 1 to 999, so the same number becomes 470 x 10^-6.
The multiple of three is the whole point, because SI prefixes step in thousands. An exponent of minus 6 is micro, so 470 x 10^-6 A simply is 470 microamps. Scientific notation cannot make that leap directly, because 10^-4 has no prefix.
The prefix ladder
Going up: kilo, mega, giga, tera, peta at 10^3, 6, 9, 12 and 15. Going down: milli, micro, nano, pico, femto at 10^-3, minus 6, minus 9, minus 12 and minus 15. Each step is a factor of a thousand, and the tool names the prefix whenever the engineering exponent lands on one.
Two habits worth keeping. Centi and deci exist but are not engineering prefixes, since they are not powers of a thousand, which is why engineering drawings use millimetres and never centimetres. And the symbol for micro is properly the Greek mu, commonly typed as u when the character is unavailable, as it is here.
A worked check you can repeat on paper
Take 0.00047 A. Slide the decimal point right in steps of three: 0.47 x 10^-3, then 470 x 10^-6. Two steps, exponent minus 6, prefix micro, so 470 microamps. The tool returns 470 x 10^-6 with the prefix named, and its scientific form 4.7 x 10^-4 for comparison.
Going large works the same: 299792458 m per s becomes 299.79 x 10^6, which reads as roughly 300 megametres per second, an unusual but perfectly valid way to state the speed of light.
Mistakes that catch people out
Reading 10^-4 as a prefix. There is none. Fix: move to the nearest multiple of three first, then read the prefix.
Mixing prefix and exponent. Writing 4.7 k x 10^3 double counts by a thousand. Fix: use a prefix or an exponent, never both.
Capitalisation errors. Capital M is mega and lower case m is milli, nine orders of magnitude apart, and both appear on the same drawings. Fix: check case before trusting any prefixed value.
Assuming the mantissa shows precision. 470 x 10^-6 says nothing about whether the trailing zero is measured. Fix: significant figures are a separate question, handled by a separate tool.
How this was checked
The converter was tested across eleven orders of magnitude. 12345 returns 1.2345 x 10^4 scientific and 12.345 x 10^3 engineering. 0.00012 returns exactly 120 x 10^-6, a case that naive floating point division renders as 120.00000000000001 and which this tool cleans correctly. The boundary cases 999 and 1000 return exponents 0 and 3 respectively, confirming the band edges, and prefix lookups were verified from femto to tera.
Related Calculators and Reference
How many of those mantissa digits you are entitled to claim is the business of the Significant Figures and Rounding Calculator. Prefixed units appear throughout the converters, including the Pressure Unit Converter spanning kPa to MPa and the Length and Distance Converter running from nanometres to kilometres. Geological time has its own ladder in the Geologic Age Unit Converter, where ka, Ma and Ga are the same thousands trick applied to years.