Scientific Notation Converter

Why scientific notation exists

Some numbers are too unwieldy to write out: the distance to the nearest star is roughly 40,140,000,000,000,000 metres, and the radius of a hydrogen atom is about 0.0000000000529 metres. Scientific notation compresses both into a tidy coefficient × 10^exponent form, so those become 4.014 × 10^16 and 5.29 × 10^-11. The exponent tells you the scale at a glance, and the coefficient carries the precision. This converter takes any number you type and shows it simultaneously in four equivalent notations, lets you control precision with significant figures, and even does arithmetic across scales.

The four notations, side by side

• Scientific: coefficient between 1 and 10 times a power of ten, e.g. 1.23 × 10^5. The standard form for any scale.
• Engineering: the same idea, but the exponent is forced to a multiple of three (…10^-6, 10^-3, 10⁰, 10³, 10⁶…) so the coefficient can run from 1 up to 999. This maps directly onto SI prefixes, and the tool labels the matching prefix — kilo (k), mega (M), micro (µ), milli (m) and so on.
• E-notation: the compact form computers and calculators use, where × 10^ is written as the letter E, e.g. 1.23E+5.
• Standard decimal: the fully written-out number, e.g. 123000.

Significant figures: precision you control

A slider sets significant figures from 1 to 12, and the coefficient in every notation is rounded to that many. Significant figures are the digits that carry real information, counted from the first non-zero digit. Rounding 1.23456 × 10^5 to three significant figures gives 1.23 × 10^5; to five it gives 1.2346 × 10^5. This matters in science because a result should not claim more precision than the measurement that produced it — reporting 4.014 × 10^16 (four figures) honestly states how well the distance is known, whereas writing all sixteen digits would imply impossible accuracy.

A worked example

Type 0.0000123. With four significant figures the tool shows scientific 1.230 × 10^-3, engineering 1.23 × 10^-3 labeled with the milli prefix, E-notation 1.230e-3, and standard 0.00123. Now drag significant figures to 2 and the coefficient tightens to 1.2 across every form at once. The engineering view immediately tells you this quantity is "about 1.2 thousandths" — which, if it were a length, you would read straight off as 1.23 millimetres.

Doing arithmetic across scales

The built-in calculator multiplies or divides two values entered in any notation. Multiplying powers of ten means adding the exponents and multiplying the coefficients; dividing means subtracting the exponents and dividing the coefficients. For example (3 × 10^8) × (2 × 10^-4) gives 6 × 10^4 — multiply 3 by 2, add 8 and −4. The tool performs this, applies your significant-figure setting, and prints the answer in all four notations, so you never have to juggle exponents by hand. It also includes a reference table of real quantities, from a proton's radius (8.5 × 10^-16 m) to the observable universe (8.8 × 10^26 m), to give those bare exponents physical meaning.

Practical use cases

• Physics and chemistry homework: convert between the notation a textbook uses and the one your calculator displays, and round answers to the right number of significant figures.
• Engineering: the engineering view's multiple-of-three exponents line up with component values and SI units, so 4.7 × 10^3 ohms reads instantly as 4.7 kΩ.
• Data and programming: decode the E-notation that spreadsheets and logs emit for very large or small numbers.

Tips and limits to keep in mind

• You can paste in several formats. The parser accepts plain decimals, E-notation (1.5e-10), and even 1.5 × 10^-10, so you rarely have to reformat before converting.
• Floating-point ceiling. Calculations use standard 64-bit floating point, which is exact and reliable for exponents up to about ±308. Beyond that range you reach the limits of the number type, so treat extreme display-only values as approximate.
• More figures isn't more accurate. Raising the significant-figure slider shows more digits but cannot recover precision the original number never had — match it to your real measurement.