Scientific Notation Converter
Free scientific notation converter. Convert between decimal form and scientific notation (a × 10ⁿ) instantly, either direction. No signup.
Converting to and from scientific notation
Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of ten, so 12,345 becomes 1.2345 × 104. This converter moves a value in either direction: type an ordinary decimal and it returns the scientific form with the coefficient and exponent separated, or type an exponent form such as 4.5e-4 and it returns the decimal.
How the converter works
In the default auto mode it inspects the text you type. If it contains an e, an x, a multiplication sign, or a caret, the value is treated as scientific input and expanded to decimal. Otherwise it is treated as a plain decimal and normalised.
Normalising uses the base-10 logarithm: the exponent is the floor of log₁₀ of the absolute value, and the coefficient is the number divided by 10 raised to that exponent. That guarantees a coefficient of at least 1 and below 10. Zero is a special case and is reported as 0 × 100.
Worked example using the default value
The input starts at 12345 in auto mode, so the converter normalises it:
| Step | Working | Result |
|---|---|---|
| Exponent | floor(log₁₀ 12345) = floor(4.0915) | 4 |
| Coefficient | 12345 ÷ 104 = 12345 ÷ 10000 | 1.2345 |
| Output | coefficient × 10 raised to the exponent | 1.2345 × 104 |
The tool lists the scientific form, the coefficient 1.2345, and the exponent 104. To return to decimal, multiply the coefficient by the power of ten: 1.2345 × 10000 = 12345, which is the original value.
Reference: powers of ten and their prefixes
| Power | Value | Prefix | Symbol |
|---|---|---|---|
| 1012 | 1,000,000,000,000 | tera | T |
| 109 | 1,000,000,000 | giga | G |
| 106 | 1,000,000 | mega | M |
| 103 | 1,000 | kilo | k |
| 10−2 | 0.01 | centi | c |
| 10−3 | 0.001 | milli | m |
| 10−6 | 0.000001 | micro | µ |
| 10−9 | 0.000000001 | nano | n |
Some quick conversions: 0.00045 becomes 4.5 × 10−4, 93,000,000 becomes 9.3 × 107, 1000 becomes 1 × 103, and 0.5 becomes 5 × 10−1. Note how a negative exponent always corresponds to a value below 1.
Common mistakes
- Misreading the exponent sign. 4.5 × 10−4 is 0.00045, while 4.5 × 104 is 45,000 — a hundred-million-fold gap.
- Leaving the coefficient at 10 or above. 12.3 × 103 should be rewritten as 1.23 × 104.
- Miscounting the shift with trailing zeros. 1,000,000 is 1 × 106, not 107.
- Mixing multiplication symbols. The parser accepts
e,x, a multiplication sign, and^, but a number like 3 10 4 with no operator cannot be read.
How do I multiply and divide numbers in scientific notation?
To multiply, multiply the coefficients and add the exponents: (2 × 103) × (3 × 104) = 6 × 107. To divide, divide the coefficients and subtract the exponents: (8 × 106) ÷ (2 × 102) = 4 × 104. If the resulting coefficient falls outside 1 to 10, shift the decimal point and adjust the exponent.
What is the scientific notation of zero?
Zero cannot be written with a coefficient between 1 and 10, because every power of ten times a normal coefficient is non-zero. The converter therefore reports it as 0 × 100 as a convention.
Does the converter accept calculator-style e notation?
Yes. Inputs such as 4.5e-4, 6.02x10^23, and 9,300,000 are all recognised. Commas inside a decimal input are stripped before parsing, and the exponent markers are normalised to a single form internally.
How many significant figures are shown?
The coefficient is kept to ten significant digits, and very small or very large decimal results fall back to exponential form rather than a long row of zeros. This keeps the output readable without inventing precision that was not in the input.
Extreme magnitudes are easier to reason about once you are comfortable with logarithms, so the logarithm calculator is a useful companion, and the unit converter handles the metric prefixes shown in the table above.