MATH · SCIENTIFIC NOTATION
Scientific Notation Calculator
Convert numbers to and from scientific notation (m × 10^e). Supports 6 significant figures for the mantissa.
1.23457 × 10^3
Decimal1234.5678
Mantissa1.23457
Exponent3
About This Calculator
Scientific notation expresses numbers as m × 10^e where 1 ≤ |m| < 10. It makes very large and very small numbers easier to read and compare, and is used throughout science, engineering, and computing.
How It Works
In Decimal → Scientific mode, enter any finite number and see it expressed in scientific notation with the mantissa rounded to 6 significant figures. In Scientific → Decimal mode, enter the mantissa and an integer exponent to get the full decimal value.
The Formula
x = m × 10^e e = floor(log₁₀|x|) m = x / 10^e
- m
- mantissa: 1 ≤ |m| < 10
- e
- exponent (integer power of 10)
Frequently Asked Questions
- How is the mantissa rounded?
- The mantissa is displayed to 6 significant figures using JavaScript's toExponential method, which implements the IEEE 754 round-half-to-even rule.
- What happens with negative numbers?
- Negative numbers produce a negative mantissa — for example, −1000 = −1 × 10^3. The exponent is derived from the absolute value.
- What is zero in scientific notation?
- Zero is a special case — it cannot be expressed as m × 10^e with 1 ≤ |m| < 10. The convention is 0 × 10^0.