Scientific Notation Converter

How the scientific notation converter works

Scientific notation writes a number as a × 10ⁿ, where the coefficient a satisfies 1 ≤ |a| < 10 and n is an integer. It is the standard way to express very large or very small measurements compactly — the mass of a proton as 1.6726 × 10⁻²⁷ kg, or the number of molecules in a mole as 6.022 × 10²³. Beyond compactness, scientific notation makes the count of significant figures unambiguous: every digit in the coefficient is significant, and the exponent tells you nothing about precision.

Converting decimal to scientific

Find the first non-zero digit. That becomes the units place of your coefficient. Count how many places the decimal point has to move to get there: moving left gives a positive exponent; moving right gives a negative one. Examples:

• 47500 — the first non-zero digit is 4. The decimal moves four places left (from after the last 0 to just after the 4), so n = 4. Result: 4.75 × 10⁴.
• 0.00042 — the first non-zero digit is 4. The decimal moves four places right, so n = −4. Result: 4.2 × 10⁻⁴.
• 3.14 — already in the range 1 ≤ |a| < 10, so the exponent is 0: 3.14 × 10⁰.

Converting scientific to decimal

Take the coefficient and shift the decimal point n places — right if n is positive (appending zeros as needed), left if n is negative (prepending zeros). 6.022 × 10²³ expands to 602200000000000000000000. 3.4 × 10⁻³ expands to 0.0034. The shift never changes the number; it only rewrites how it looks on the page.

Engineering notation

Engineering notation is a variant of scientific notation with one constraint added: the exponent must be a multiple of three. This aligns with SI prefixes — 10³ is kilo, 10⁶ is mega, 10⁻³ is milli, 10⁻⁶ is micro, and so on. In engineering notation, the coefficient can be anywhere from 1 up to 1000, not just 1 to 10.

Example: 47500 in scientific notation is 4.75 × 10⁴, but in engineering notation it is 47.5 × 10³. The second form reads naturally as "47.5 kilo-somethings." Likewise, 0.00042 scientific is 4.2 × 10⁻⁴, but engineering form is 420 × 10⁻⁶ (420 micro-somethings).

This tool shows both forms whenever you convert a decimal to scientific, because the choice between them is stylistic and context-dependent: physics papers prefer scientific; electrical-engineering datasheets prefer engineering.

Edge cases

Negative numbers. The sign attaches to the coefficient. −0.0056 becomes −5.6 × 10⁻³. The exponent never carries the sign of the number.

Zero. Strict scientific notation cannot represent zero (log of 0 is undefined). We show 0 × 10⁰ as a convention, but you rarely need scientific notation for exactly zero.

Numbers already in scientific form. If you enter 1.2e3 in the "to scientific" direction, we normalise it — the result is still 1.2 × 10³.

Significant figures. This converter preserves the digits you entered but does not add or remove precision. If you enter 47500 and convert to scientific, the result is 4.75 × 10⁴ (three sig figs). If you wanted 4.7500 × 10⁴ (five sig figs), you would need to enter 47500. with the trailing decimal, or enter the scientific form directly.

What this calculator is not

This tool converts notation; it does not perform arithmetic in scientific notation. To multiply 3 × 10⁴ by 2 × 10⁵, you multiply coefficients (6) and add exponents (9) to get 6 × 10⁹, but that is a separate operation. It also does not perform significant-figure-aware rounding. For sig fig analysis, use our Significant Figures Calculator, which applies the five standard rules to any numeric input.