Scientific Notation Converter
Convert any number into scientific notation (a × 10^b) and engineering notation (b is a multiple of 3).
Type any decimal number. Both scientific and engineering forms are shown.
Scientific notation-
Engineering notation-
E-notation-
Decimal-
How is this calculated?
Scientific: n = a × 10^b with 1 ≤ |a| < 10. Engineering: b is rounded down to the nearest multiple of 3 and a is rescaled. E-notation uses "e" for the × 10^ shorthand.
About the Scientific Notation Converter
Scientific notation is a compact way to write very large or very small numbers as a times 10 to the power b, with the mantissa a satisfying 1 less than or equal to the absolute value of a, which is less than 10. This converter also outputs engineering notation, where the exponent is a multiple of 3 and lines up with SI prefixes.
The tool above accepts any decimal input and shows four parallel forms: standard scientific, engineering, programmer-style E notation, and the original decimal. Adjust the significant figures slider from 1 to 15 to match the precision of your measurement. Inputs use plain JavaScript Number arithmetic, so values inside roughly 10 to the plus or minus 308 are handled cleanly.
How the formula works
Scientific: n = a x 10^b, 1 <= |a| < 10, b is an integer Engineering: n = a' x 10^b', b' = floor(b / 3) x 3, a' = n / 10^b' E notation: "1.5e6" is shorthand for 1.5 x 10^6 Round trip: decimal value is preserved at the chosen significant figures
- a = mantissa (or coefficient), restricted to the half-open interval [1, 10) for positive numbers so the form is unique.
- b = exponent, the integer power of 10 needed to recover the original magnitude. Negative for numbers below 1.
- Significant figures = how many leading digits of a you keep. Trailing zeros in a are significant; only the rounded mantissa is displayed.
- Engineering b prime = the next-lowest multiple of 3, so the result reads as kilo (10^3), mega (10^6), micro (10^-6), and so on.
Worked example: speed of light
The defined speed of light in vacuum is c = 299,792,458 m/s. Convert it to scientific notation at 4 significant figures.
- Take the absolute value: 299,792,458.
- Find the exponent: floor of log base 10 of 299,792,458 = 8.
- Divide by 10 to the 8: 299,792,458 / 100,000,000 = 2.99792458.
- Round to 4 significant figures: a = 2.998.
- Recombine: c is approximately 2.998 times 10 to the 8 m/s, or 2.998e8 in E notation.
- Engineering form: 8 is already a multiple of 3 plus 2, so use exponent 6 and shift the mantissa: c is approximately 299.8 times 10 to the 6 m/s, read as 299.8 megametres per second.
Result: 2.998 x 10^8 m/s (scientific), 299.8 x 10^6 m/s (engineering), 2.998e8 (E notation). All three encode the same physical quantity at 4 significant figures.
SI prefix reference
| Prefix | Symbol | Power of 10 | Example |
|---|---|---|---|
| tera | T | 10^12 | 1 TB of storage = 10^12 bytes (SI) |
| giga | G | 10^9 | 3 GHz CPU clock = 3 x 10^9 Hz |
| mega | M | 10^6 | 2 MW power plant = 2 x 10^6 W |
| kilo | k | 10^3 | 5 km distance = 5 x 10^3 m |
| (none) | - | 10^0 | 1 metre, 1 second, 1 ohm |
| milli | m | 10^-3 | 250 mL = 2.5 x 10^-1 L |
| micro | u | 10^-6 | 50 us latency = 5 x 10^-5 s |
| nano | n | 10^-9 | 520 nm green light = 5.2 x 10^-7 m |
| pico | p | 10^-12 | 3.3 pF capacitor = 3.3 x 10^-12 F |
| femto | f | 10^-15 | 1 fs pulse = 10^-15 s |
Source: NIST Special Publication 811 (Guide for the Use of the International System of Units).
Common pitfalls
- Misreading E notation. 1.5e6 is 1.5 x 10^6, not 1.5 x e^6. The lower case e is the times 10 to the power operator in software, not Euler's number.
- Forgetting the mantissa bound. 12.5 x 10^4 is correct arithmetic but not scientific notation. The unique form is 1.25 x 10^5.
- Significant figures vs decimal places. 0.00450 has 3 significant figures (4, 5, 0). In scientific form it is 4.50 x 10^-3, which makes the trailing zero unambiguous.
- Mixing engineering and scientific. Engineering notation pins the exponent to multiples of 3 so the mantissa can be 1 to 999. Do not assume the mantissa is below 10.
- Floating point overflow. JavaScript Number maxes out near 1.8 x 10^308. For larger magnitudes (combinatorics, cosmology) use BigInt or a library like decimal.js.
Related tools and glossary
Frequently asked questions
What is scientific notation?
Scientific notation writes a number as a times 10 to the power b, where the mantissa a satisfies 1 less than or equal to the absolute value of a, which is less than 10, and the exponent b is an integer. The speed of light 299,792,458 m/s becomes 2.998 times 10 to the 8 in 4 significant figures. The form makes very large or very small magnitudes readable and comparable.
What is the difference between scientific and engineering notation?
Scientific notation allows any integer exponent. Engineering notation restricts the exponent to multiples of 3, which line up with SI prefixes such as kilo, mega, giga, micro, and nano. 47,000 ohms is 4.7 times 10 to the 4 scientifically but 47 times 10 to the 3 in engineering form, read as 47 kiloohms.
How do I read E notation like 1.5e6?
E notation is a typing shortcut used in calculators, spreadsheets, and code. 1.5e6 means 1.5 times 10 to the 6, equal to 1,500,000. 2.3e-4 means 2.3 times 10 to the negative 4, equal to 0.00023. The lower case e or upper case E does not refer to Euler's number here, only to the times 10 to the power operator.
How many significant figures should I keep?
Match the precision of your least precise input. 3 significant figures suit most engineering work, 4 to 6 cover laboratory measurements, and 9 or more are reserved for fundamental constants. The CODATA 2018 speed of light is 299,792,458 m/s exact by definition; a measured pressure of 101.3 kPa is only 4 significant figures so the answer cannot be more precise.
Why does scientific notation make multiplication easier?
When multiplying numbers in the form a times 10 to the b, you multiply the mantissas and add the exponents. (3 times 10 to the 4) times (2 times 10 to the 5) equals 6 times 10 to the 9. Division subtracts the exponents. This lets you mental math huge magnitudes that would otherwise overflow normal arithmetic.
Sources
- NIST Special Publication 811 (2008, current edition). Guide for the Use of the International System of Units (SI), prefix table in Section 4.
- BIPM (2019). The International System of Units (SI Brochure), 9th edition.
- CODATA 2018. Recommended Values of the Fundamental Physical Constants.
- Mozilla Developer Network. Number.prototype.toPrecision.