Scientific notation
1.23 × 10^6
Value written as a × 10ⁿ.
Mathematics · Numbers & everyday maths
Scientific notation calculator — decimal ↔ a × 10ⁿ
Convert a finite decimal number to scientific notation, or reconstruct the decimal value from a coefficient and base-10 exponent.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
03
Results
Coefficient a
1.23
Exponent n
6
Results show up to four significant digits for readability; internal calculations retain full precision.
See calculation details
01Scientific notation
Formula
a×10ⁿ = a × 10^nSubstitution
1.23 × 10^6Result
1.23 × 10^6
01Formulas and symbols
Formulas used
x
x = a × 10ⁿ
1 ≤ |a| < 10 for x ≠ 0
Scientific notation represents a number as a coefficient multiplied by a power of ten.
| Symbol | Meaning |
|---|---|
| x | Decimal value x |
| a | Coefficient a |
| n | Exponent n |
| a×10ⁿ | Scientific notation |
02Validation example
Reference numerical case
- 1,230,000 = 1.23 × 10^6, and 1.23 × 10^6 converts back to 1,230,000.
03Move the decimal point by powers of ten
The exponent counts how many decimal places are moved to leave one non-zero digit before the decimal point. The reverse conversion multiplies the coefficient by 10ⁿ.
04Limits and conventions
The conversion uses finite JavaScript numbers, so extremely large or tiny exponents outside the representable range are rejected.
05Common mistakes
Moving the decimal point left gives a positive exponent for large numbers; moving it right gives a negative exponent for values between −1 and 1.
06Practical questions
What coefficient range is standard scientific notation?
For a non-zero number, the normalized coefficient has magnitude at least 1 and less than 10.
How is zero written?
This calculator uses 0 × 10^0 as a simple canonical representation of zero.