Scientific Notation Converter
Convert any number to scientific notation instantly. Enter a standard decimal number to see it expressed as a coefficient × 10^exponent.
What Is Scientific Notation?
Scientific notation is a standardized way to write very large or very small numbers. Any number can be expressed as a coefficient (between 1 and 10) multiplied by a power of 10. The format is: a × 10^n, where the coefficient a satisfies 1 ≤ |a| < 10.
Scientists use this notation because it compactly represents extreme values and makes arithmetic operations like multiplication and division much easier. The speed of light (299,792,458 m/s) is more clearly written as 2.998 × 10^8. The mass of an electron (0.000000000000000000000000000000911 kg) is written as 9.11 × 10^−31.
Scientific Notation Examples
| Standard Form | Scientific Notation | Context |
|---|---|---|
| 1,000,000 | 1.0 × 10^6 | One million |
| 299,792,458 | 2.998 × 10^8 | Speed of light (m/s) |
| 0.001 | 1.0 × 10^−3 | One thousandth |
| 0.000001 | 1.0 × 10^−6 | One micron |
| 6,022,000,000,000,000,000,000,000 | 6.022 × 10^23 | Avogadro's number |
| 9,460,730,472,580,800 | 9.461 × 10^15 | Light year (meters) |
Significant Figures in Scientific Notation
Scientific notation naturally communicates significant figures. The number of digits in the coefficient indicates how precisely the value is known. 3.0 × 10^4 has 2 significant figures; 3.00 × 10^4 has 3. Writing 30,000 in standard form ambiguously might mean anywhere from 1 to 5 significant figures — but 3.0 × 10^4 is unambiguous.
In scientific and engineering work, always use the correct number of significant figures in your coefficient. Reporting more digits than your measurement precision supports is misleading. Reporting fewer loses information. The coefficient in scientific notation is where significant figure discipline is enforced.
Frequently Asked Questions
What is scientific notation?
Scientific notation expresses any number as a coefficient between 1 and 10, multiplied by a power of 10. Format: a × 10^n, where 1 ≤ |a| < 10. Examples: 1,234,567 = 1.234567 × 10^6. 0.00042 = 4.2 × 10^−4. 602,200,000,000,000,000,000,000 (Avogadro's number) = 6.022 × 10^23. Scientific notation makes very large and very small numbers manageable, avoids ambiguity about significant figures, and simplifies multiplication and division of extreme values.
How do I convert a number to scientific notation?
Step 1: Identify the first non-zero digit. Step 2: Place the decimal point after that digit to form the coefficient. Step 3: Count how many places you moved the decimal — this is the exponent. Moving left (large numbers) gives positive exponents. Moving right (small numbers) gives negative exponents. Example: 45,000 → move decimal 4 places left → 4.5 × 10^4. Example: 0.00067 → move decimal 4 places right → 6.7 × 10^−4.
What does E notation mean (like 1.5E6)?
E notation is computer shorthand for scientific notation, used because typing superscripts is difficult in plain text. 1.5E6 means 1.5 × 10^6 = 1,500,000. 3.2E−4 means 3.2 × 10^−4 = 0.00032. You will see E notation on scientific calculators, in programming languages (Python, JavaScript, C), and in spreadsheets. It is functionally identical to standard scientific notation — just a different way to write it.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. Example: (3 × 10^4) × (2 × 10^3) = (3 × 2) × 10^(4+3) = 6 × 10^7. If the resulting coefficient is ≥ 10, adjust: 15 × 10^7 = 1.5 × 10^8. For division: divide the coefficients and subtract the exponents. (6 × 10^8) / (3 × 10^3) = 2 × 10^5. This is why scientific notation is preferred in science — operations that would be error-prone with long decimals become straightforward arithmetic.