Scientific Notation Tool
Enter decimal or scientific-notation values to convert formats, perform arithmetic or compare numbers. Choose significant figures, scientific or engineering notation and exponent display. Explore coefficient and exponent breakdowns, an interactive power scale, comparison results and charts.
| Format | Value | Copy |
|---|
Table of Contents
Highlights
- Convert between scientific, engineering, E and decimal notation.
- Calculate sums, differences, products, quotients and powers.
- Compare two values with ratios, differences and ordering.
- Choose 3–15 significant figures or automatic precision.
- Explore exponent charts, interactive powers and downloadable results.
How Scientific Notation Tool Works?
Scientific notation expresses a non-zero number as a coefficient multiplied by a power of ten. The coefficient has an absolute value of at least 1 and less than 10; a negative exponent represents a value smaller than one. For example:
Engineering notation uses exponents divisible by three, allowing the coefficient to range from 1 to less than 1000 in absolute value. E notation writes the same power as 6.02214076e+23. Choose automatic precision (up to 12 significant figures) or 3, 4, 5, 6, 8, 10, 12 or 15 figures. The notation display can use × 10 with an exponent or E notation.
| Operation | Rule |
|---|---|
| Multiply | Multiply coefficients and add exponents. |
| Divide | Divide coefficients and subtract exponents, provided the divisor is not zero. |
| Add or subtract | Express terms with a common exponent before combining coefficients. |
| Power | Raise A to the numerical power B, where a real finite result exists. |
| Compare | Show A relative to B, A − B, A ÷ B and the absolute difference. |
Outputs include scientific, E, engineering and decimal representations, coefficient, exponent and order of magnitude. A nearby-exponent chart and interactive powers-of-ten scale visualise size.
Practical Use Cases
Scientists: Express measurements and constants containing extremely large or small values, such as 6.02214076e23, and view their coefficient and exponent separately.
Engineers: Use engineering notation with exponents in multiples of three to present quantities consistently, and choose a suitable significant-figure display.
Students: Practise multiplying, dividing, adding and subtracting numbers written using powers of ten, then inspect equivalent representations.
Data analysts: Compare two differently scaled figures using their difference, ratio and ordering, or export the displayed results as CSV or JSON.
Educators: Demonstrate how an exponent changes a number’s scale with the interactive slider and highlighted exponent chart.
Accuracy and Limitations
Calculations use JavaScript IEEE 754 double-precision numbers, giving approximately 15–17 significant decimal digits, not arbitrary precision. Inputs and results must remain finite, roughly up to 1.8 × 10308, while very small non-zero values can underflow below approximately 5 × 10−324. The tool rejects invalid values, division by zero, non-real or overflowing power results and detected multiplication, division or power underflow. The 3–15 significant-figure selection controls displayed rounding, not the precision of arithmetic. Decimal expansion is shortened when the exponent exceeds ±70, and the interactive power slider covers exponents −30 to +30.
