Scientific Notation Converter
Convert between standard numbers and scientific notation (a × 10ⁿ) instantly.
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What Is Scientific Notation?
Scientific notation expresses numbers as a coefficient (between 1 and 10) multiplied by a power of 10: a × 10ⁿ, where 1 ≤ |a| < 10. It is the standard way to write very large or very small numbers concisely in science and engineering.
Converting to Scientific Notation
1. Move the decimal point until you have a number between 1 and 10 (the coefficient). 2. Count the number of positions moved — this is the exponent. Moving left means positive exponent (large number); moving right means negative exponent (small number). Example: 45,678 → 4.5678 × 10⁴ (decimal moved 4 places left).
Converting From Scientific Notation
Multiply the coefficient by 10 raised to the exponent. Positive exponent: move decimal right. Negative exponent: move decimal left. Example: 4.5678 × 10⁻⁵ → 0.000045678 (decimal moved 5 places left).
Operations in Scientific Notation
Multiplication: multiply coefficients, add exponents. Division: divide coefficients, subtract exponents. Addition/subtraction: first convert to the same exponent, then operate on coefficients.
Real-World Scale
The diameter of a hydrogen atom is ~1.2 × 10⁻¹⁰ m. The distance from Earth to the Sun is ~1.5 × 10¹¹ m. The national debt is ~$3.5 × 10¹³. Scientific notation makes these extreme scales comparable and easy to work with.
Worked Example: Dividing in Scientific Notation
Problem: Divide (8.4 × 10⁹) by (2.1 × 10³).
Step 1 — Divide the coefficients: 8.4 ÷ 2.1 = 4.
Step 2 — Subtract the exponents: 10⁹ ÷ 10³ = 10^(9−3) = 10⁶.
Step 3 — Combine: 4 × 10⁶ = 4,000,000. The coefficient 4 is already between 1 and 10, so the answer is already in proper scientific notation.
Scientific Notation Examples by Scale
| Quantity | Standard Form | Scientific Notation |
|---|---|---|
| Speed of light (m/s) | 300,000,000 | 3.0 × 10⁸ |
| Avogadro's number | 602,200,000,000,000,000,000,000 | 6.022 × 10²³ |
| Electron mass (kg) | 0.000000000000000000000000000000911 | 9.11 × 10⁻³¹ |
| One nanometer (m) | 0.000000001 | 1.0 × 10⁻⁹ |
Frequently Asked Questions
4.5 × 10⁻⁵. The decimal moved 5 places right to get a coefficient between 1 and 10.
6.5 × 10⁶. The decimal moved 6 places left.
Multiply the coefficients and add the exponents: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷.
It simplifies working with very large or very small numbers, avoids writing many zeros, and makes comparisons easier in science and engineering.
The number between 1 (inclusive) and 10 (exclusive). In 3.7 × 10⁵, the coefficient is 3.7.
You must first convert both numbers to the same exponent before adding coefficients. Example: (3.5 × 10⁴) + (2.0 × 10³) = (3.5 × 10⁴) + (0.2 × 10⁴) = 3.7 × 10⁴. Then check whether the result needs to be re-normalized.
In scientific notation, the exponent can be any integer. In engineering notation, the exponent is always a multiple of 3 (e.g., 10³, 10⁶, 10⁹). Engineering notation aligns with SI prefixes: kilo (10³), mega (10⁶), giga (10⁹), milli (10⁻³), micro (10⁻⁶).