Scientific Notation Calculator
Convert a number to scientific notation, or convert scientific notation back to a decimal number.
About the Sci. Notation Calculator
Scientific notation compactly represents very large or very small numbers as a value between 1 and 10 multiplied by a power of ten — essential in physics, chemistry, and engineering. This calculator converts a regular decimal number into scientific notation, or converts scientific notation back into a standard decimal.
How It Works
Converting to scientific notation, the calculator expresses the number using JavaScript's exponential notation, which normalizes it to a single leading digit followed by a decimal fraction and a power of ten. Converting from scientific notation, it parses the "e" notation format directly back into a plain decimal number.
Scientific Notation: N = a × 10^b, where 1 ≤ |a| < 10. Example format: 6.5e6 means 6.5 × 10⁶.
Worked example
Scenario: Writing 6,500,000 in scientific notation.
- Move the decimal point until one non-zero digit is left of it: 6.5.
- Count the places moved: 6 to the left.
- Result: 6.5 × 10^6 (6.5e6).
Result: 6,500,000 = 6.5 × 10^6.
How scientific notation works
Scientific notation writes a number as a coefficient multiplied by a power of ten: 6,250,000 becomes 6.25 × 106, while 0.00042 becomes 4.2 × 10−4. In normalized scientific notation, the coefficient has an absolute value from 1 up to, but not including, 10.
Tips and common mistakes
- Small numbers get negative exponents: 0.000123 = 1.23 × 10^−4.
- In 'from' mode you can type 3.2e5 or 3.2 × 10^5.
- Most calculators and spreadsheets display E-notation: 6.5E6 means 6.5 × 10^6.
Assumptions & Limitations
- Uses the 'e' notation format (like 3.2e5) as both the input and output format for scientific notation, matching how calculators and programming languages commonly represent it.
- Assumes standard decimal input for the 'to scientific notation' direction.
- Extremely large or small numbers may already be displayed in scientific notation by the browser before conversion, which is expected behavior for numbers beyond typical decimal display ranges.