Scientific Notation Calculator
Convert any number to scientific, engineering and E notation with chosen significant figures, or expand a × 10ⁿ back to a plain decimal — exactly, no float noise.
Scientific Notation Calculator: with the default inputs, scientific notation is 2.998 × 10⁸.
Any decimal, e.g. 299792458 or 0.00000015.
Digits are only dropped, never padded: 5 stays 5, not 5.000.
The coefficient in a × 10ⁿ, ideally between 1 and 10.
- Standard (decimal) form
- 299800000
- Engineering notation
- 299.8 × 10⁶Exponent a multiple of 3, matching kilo / mega / milli / micro.
- E notation
- 2.998e8The form calculators and spreadsheets use.
- Order of magnitude
- 8The power of ten; blank for zero.
Assumptions
- Digits come from the number's shortest exact decimal representation, so 0.1 is 1 × 10⁻¹, not 1.0000000000000000555 × 10⁻¹.
- Significant figures are only ever reduced, never padded with zeros.
| Power of ten | Written out | Prefix | Symbol | |
|---|---|---|---|---|
| 10¹² | 1 000 000 000 000 | tera | T | |
| 10⁹ | 1 000 000 000 | giga | G | |
| 10⁶ | 1 000 000 | mega | M | ◀ your number's engineering exponent |
| 10³ | 1 000 | kilo | k | |
| 10⁰ | 1 | — | ||
| 10⁻³ | 0.001 | milli | m | |
| 10⁻⁶ | 0.000 001 | micro | µ | |
| 10⁻⁹ | 0.000 000 001 | nano | n | |
| 10⁻¹² | 0.000 000 000 001 | pico | p |
Engineering notation uses only these exponents, which is why it reads straight off as kilo-, mega- or milli- something.
How this is worked out
The formula
Scientific notation: a × 10ⁿ with 1 ≤ |a| < 10 and n an integer Engineering notation: a × 10ⁿ with n a multiple of 3 and 1 ≤ |a| < 1000 E notation: aEn (2.998e8 = 2.998 × 10⁸) Order of magnitude = n = ⌊log₁₀|x|⌋
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- Direction
- Choose one of 2 options.Number → scientific notation · Mantissa and exponent → number
- Number
- Any decimal, e.g. 299792458 or 0.00000015.defaults to 299792458
- Significant figures to keep
- Digits are only dropped, never padded: 5 stays 5, not 5.000.from 1 to 15 · whole numbers only · defaults to 4
- Mantissa (a)
- The coefficient in a × 10ⁿ, ideally between 1 and 10.defaults to 2.99792458
- Exponent (n)
- A number.from -300 to 300 · whole numbers only · defaults to 8
What you get back
- Scientific notationmain answer
- Standard (decimal) form
- Engineering notation
- Exponent a multiple of 3, matching kilo / mega / milli / micro.
- E notation
- The form calculators and spreadsheets use.
- Order of magnitude
- The power of ten; blank for zero.
What this assumes
- Digits come from the number's shortest exact decimal representation, so 0.1 is 1 × 10⁻¹, not 1.0000000000000000555 × 10⁻¹.
- Significant figures are only ever reduced, never padded with zeros.
About this calculator
Scientific notation writes a number as a mantissa between 1 and 10 times a power of ten: the speed of light is 2.998 × 10⁸ m/s rather than 299,800,000 m/s, and a hydrogen atom's radius is 5.3 × 10⁻¹¹ m rather than 0.000000000053 m. Two things become obvious at a glance — the size (the exponent) and the precision (how many digits you kept).
How to use it
To convert a number, type it and choose how many significant figures to keep; the calculator moves the decimal point, counts the moves, rounds the mantissa and reports the scientific, engineering and E forms plus the order of magnitude. To go the other way, switch the direction and enter the mantissa and exponent; you get the number written out in full, with every zero.
The rule
Slide the decimal point until exactly one non-zero digit sits in front of it. Each place you slid it to the left adds 1 to the exponent (big numbers get positive exponents); each place to the right subtracts 1 (small numbers get negative exponents). Moving the point back the other way recovers the original number, which is what the reverse mode does.
Significant figures
Scientific notation is the honest way to show precision. "300,000,000" might be measured to one digit or to nine; 3.00 × 10⁸ says clearly that three digits are trustworthy. This calculator only ever drops digits, never pads them, so 5 stays 5 rather than becoming 5.000. If rounding carries over (9.997 at three figures becomes 10.0), the exponent adjusts automatically.
Engineering notation
Engineers prefer exponents that are multiples of 3 because those line up with metric prefixes: 47 × 10³ Ω is 47 kΩ, 3.3 × 10⁻⁶ F is 3.3 µF. The mantissa then runs from 1 up to 999 instead of 1 to 9.99.
Common mistakes
- Getting the sign of the exponent backwards. Small numbers (less than 1) have negative exponents.
- Leaving more than one digit before the point (29.98 × 10⁷ is correct in value but not normalized).
- Reading 2.998e8 as 2.998 × e⁸ — the "e" here means "times ten to the", not Euler's number.
Frequently asked questions
▸How do I write a number in scientific notation?
Move the decimal point so one non-zero digit is in front of it, and count the moves. 4,500 → 4.5 with 3 moves left, so 4.5 × 10³. 0.0045 → 4.5 with 3 moves right, so 4.5 × 10⁻³.
▸What does 2.998e8 mean?
2.998 × 10⁸, or 299,800,000. The 'e' stands for 'times ten to the power of' and has nothing to do with the constant e.
▸What's the difference between scientific and engineering notation?
Scientific notation keeps the mantissa between 1 and 10; engineering notation restricts the exponent to multiples of 3 so it matches kilo, mega, milli and micro, letting the mantissa run up to 999.
▸What is an order of magnitude?
The power of ten in scientific notation — roughly, how many digits long the number is. Two numbers differ by an order of magnitude when one is about ten times the other.
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