Scientific Notation Calculator
Enter a number in plain decimal or E notation and get every standard form at once: normalized scientific notation, E notation, engineering notation, the exact decimal expansion, and the significant-figure count. Conversion is exact — no floating-point rounding.
Convert a number
Example: 0.00052 is 5.2 × 10^-4.
Why scientific notation exists
Very large and very small quantities are unreadable — and error-prone — as strings of zeros. Scientific notation factors every number into a coefficient between 1 and 10 and a power of ten, so magnitude becomes a single glanceable exponent. The speed of light, 299,792,458 m/s, is 2.99792458 × 10^8; a 0.00052 m wire diameter is 5.2 × 10^-4, or 5.2e-4 in the E notation used by programming languages, spreadsheets, and calculators.
Converting in both directions
To normalize a number, move the decimal point until exactly one nonzero digit remains in front
of it, counting the places moved: each place left adds one to the exponent, each place right
subtracts one. To expand notation back, reverse the process —
1.23456e4 expands to 12345.6. This page's converter does both, and every example
in this text is generated by the same tested code.
Engineering notation and unit prefixes
Engineers restrict the exponent to multiples of three so numbers map directly onto SI prefixes: 45,000 Hz reads as 45 × 10^3 — that is, 45 kHz. The same value in strict scientific notation (4.5 × 10^4) is mathematically identical but does not line up with a prefix, which is why oscilloscopes and datasheets prefer the engineering form.
Frequently asked questions
What is normalized scientific notation?
One nonzero digit before the decimal point, times a power of ten: 0.00052 becomes 5.2 × 10⁻⁴ and 299,792,458 becomes 2.99792458 × 10⁸. E notation writes the same thing compactly: 5.2e-4.
How is engineering notation different?
The exponent is restricted to multiples of 3 so it lines up with unit prefixes (kilo, mega, milli, micro). 45,000 is 4.5 × 10⁴ in scientific notation but 45 × 10³ in engineering notation — i.e. 45 k.
Do trailing zeros count as significant figures?
After a decimal point, yes: 0.00520 has three significant figures and this calculator keeps the trailing zero (5.20 × 10⁻³). In a bare integer like 1200 the trailing zeros are treated as placeholders, giving 1.2 × 10³.
Why does this tool use string math instead of floating point?
Floating-point conversion silently rounds long numbers (123456789012345678 cannot be stored exactly in a double). This converter manipulates the decimal digits as text, so every conversion is exact at any length up to its input limit.
Values are processed locally in your browser and never transmitted. The conversion is implemented as tested, typed string-math functions — see the methodology page.