Scientific Notation Converter
Scientific notation writes any number as a coefficient between 1 and 10 multiplied by a power of ten, which keeps very large and very small numbers readable and comparable. A bacterium's size, a country's population, the distance to a star — all become a tidy a × 10^n. This converter takes a plain decimal and returns the normalised coefficient and the exponent, so you can express a number in standard form, compare orders of magnitude, or prepare a value for a calculator or spreadsheet.
Calculate
Default result: 1.234500
Scientific Notation Converter · Result
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Coefficient (a, where 1 ≤ |a| < 10)
12345
- Power of ten (n)
- 4
Reviewed by the calculators.dev team · Last updated 2026-06-23
How to calculate
Type any number into the box. The converter finds the power of ten by taking the base-10 logarithm and rounding down, which tells you how many places the decimal point must move. It then divides the number by that power of ten to get the coefficient, a value between 1 and 10. For 12345 the exponent is 4 and the coefficient is 1.2345, so the number is 1.2345 × 10^4. Negative numbers keep their sign on the coefficient, and the result updates instantly.
For a non-zero value, the exponent is n = ⌊log₁₀(|value|)⌋ and the coefficient is a = value ÷ 10^n, which lands a in the range 1 ≤ |a| < 10. Numbers below one give a negative exponent (0.0045 = 4.5 × 10^−3), and zero is the single special case, written as 0 × 10^0 because it has no logarithm.
Example calculation
To write 12345 in scientific notation, move the decimal point left until one non-zero digit remains in front of it: 1.2345. The point moved four places, so the exponent is 4, giving 1.2345 × 10^4. Multiplying 1.2345 by ten thousand returns the original 12345, confirming the conversion.
- coefficient
- 1.2345
- exponent
- 4
Assumptions
- The coefficient is normalised to a single non-zero digit before the decimal point (1 ≤ |a| < 10), the standard form used in science.
- Very large or very small magnitudes can carry tiny binary-floating-point rounding in the coefficient's trailing digits.
- Zero is written as 0 × 10^0, since it has no defined power-of-ten representation.
Common mistakes
- Leaving more than one digit before the decimal point (12.345 × 10^3), which is valid arithmetic but not normalised scientific notation.
- Getting the exponent sign backwards for small numbers — 0.0045 is 4.5 × 10^−3, not 10^3.
- Counting the decimal-point moves in the wrong direction, which flips the exponent's sign.
Frequently asked questions
How do I write a number in scientific notation?
Move the decimal point until one non-zero digit remains in front of it; the number of places moved is the exponent. 12345 becomes 1.2345 × 10^4.
What does a negative exponent mean?
A negative exponent marks a number smaller than one. 0.0045 is 4.5 × 10^−3, because the decimal point moves three places to the right to reach 4.5.
Why must the coefficient be between 1 and 10?
Normalised scientific notation keeps exactly one non-zero digit before the decimal point, which makes orders of magnitude easy to compare at a glance.
How is zero written in scientific notation?
Zero is the special case 0 × 10^0. It has no power-of-ten form because there is no exponent that turns a non-zero coefficient into zero.