Scientific Notation Calculator
Convert any number to or from scientific notation. Enter a standard number or a number in scientific notation (e.g. 3.5e8) to convert.
How Scientific Notation Calculator works
What is scientific notation?
Scientific notation expresses numbers as a coefficient between 1 and 10 multiplied by a power of 10. For example, 450,000 = 4.5 × 10^5, and 0.003 = 3 × 10^-3. This notation makes very large and very small numbers easier to read, compare, and calculate with.
Converting to scientific notation
To convert a number: move the decimal point until you have a number between 1 and 10. Count how many places you moved it — this is the exponent. If you moved the decimal left, the exponent is positive. If right, it is negative. Example: 6,370,000 → 6.37 (moved 6 places left) → 6.37 × 10^6.
E notation
E notation is a shorthand used in calculators and programming. 4.5e5 means 4.5 × 10^5 = 450,000. The "e" stands for "exponent of 10". Negative exponents work the same way: 3e-4 = 3 × 10^-4 = 0.0003.
Arithmetic in scientific notation
Multiplication: multiply coefficients and add exponents. (3 × 10^4) × (2 × 10^3) = 6 × 10^7. Division: divide coefficients and subtract exponents. Addition/subtraction: align exponents first, then add or subtract coefficients. The calculator handles all normalisation automatically.
Frequently asked questions
How do I write a number in scientific notation?
Move the decimal point to get a number between 1 and 10. Count the number of places moved — that becomes the power of 10. Moved left = positive exponent, moved right = negative. Example: 93,000,000 → 9.3 × 10^7 (moved 7 places left).
What does "e" mean in scientific notation?
The "e" in e-notation means "× 10 to the power of". So 3.5e8 means 3.5 × 10^8 = 350,000,000. This shorthand is used by calculators, spreadsheets, and programming languages.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. For example: (4 × 10^3) × (2 × 10^5) = 8 × 10^8. If the coefficient ends up ≥ 10, adjust: (5 × 10^3) × (3 × 10^4) = 15 × 10^7 = 1.5 × 10^8.
What is 1 million in scientific notation?
1,000,000 = 1 × 10^6. One billion = 1 × 10^9. One trillion = 1 × 10^12. The exponent tells you the number of zeros after the 1.
How do I add numbers in scientific notation?
First make the exponents the same, then add the coefficients. For example: 3 × 10^4 + 5 × 10^3 = 3 × 10^4 + 0.5 × 10^4 = 3.5 × 10^4. The key step is converting to a common power of 10 before adding.
Why do scientists use scientific notation?
Scientific notation makes very large and small numbers manageable. The speed of light is 299,792,458 m/s, or 3.0 × 10^8 m/s. A hydrogen atom radius is 0.000000000053 m, or 5.3 × 10^-11 m. It also makes multiplication and division much easier by working with exponents.
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