Scientific Notation Calculator
Convert between standard and scientific notation with step-by-step solutions
Examples: 45000, 0.00023, 300000000, 0.0000056
How to Use This Calculator
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Standard to Scientific Notation
Enter any number in standard form (like 45000 or 0.00023) and the calculator will convert it to scientific notation (a × 10ⁿ format).
Example Conversions:
- 45000 → 4.5 × 10⁴
- 0.00023 → 2.3 × 10⁻⁴
- 300000000 → 3 × 10⁸ (speed of light in m/s)
- 0.0000000016 → 1.6 × 10⁻⁹ (nano scale)
Scientific to Standard Notation
Enter the coefficient and exponent separately, and the calculator will convert scientific notation back to standard form.
Example Conversions:
- 4.5 × 10⁴ → 45000
- 2.3 × 10⁻⁴ → 0.00023
- 6.022 × 10²³ → 602200000000000000000000 (Avogadro's number)
- 1.6 × 10⁻¹⁹ → 0.00000000000000000016 (electron charge)
Understanding Scientific Notation
Scientific notation expresses numbers as: a × 10ⁿ
- Coefficient (a): A number between 1 and 10 (e.g., 4.5)
- Base: Always 10
- Exponent (n): Positive for large numbers, negative for small numbers
Key Rules:
- Positive exponent → move decimal right (large number)
- Negative exponent → move decimal left (small number)
- Exponent shows how many places to move the decimal
Real-World Applications
Astronomy:
Distance to stars: 4.2 × 10¹³ km to nearest star
Physics:
Speed of light: 3 × 10⁸ m/s
Chemistry:
Avogadro's number: 6.022 × 10²³ particles/mole
Biology:
Size of bacteria: 2 × 10⁻⁶ meters
Frequently Asked Questions
What is scientific notation?
Scientific notation is a way to express very large or very small numbers compactly using powers of 10. It's written as a × 10ⁿ, where 'a' is a number between 1 and 10, and 'n' is an integer exponent.
Why use scientific notation?
Scientific notation makes it easier to work with extremely large numbers (like distances in space) or extremely small numbers (like atomic sizes). It's more compact, easier to read, and simplifies calculations involving multiplication and division.
How do I convert to scientific notation?
Move the decimal point until you have a number between 1 and 10. Count how many places you moved it. That count is your exponent. If you moved left, the exponent is positive. If you moved right, it's negative. For example: 45000 → move decimal 4 places left → 4.5 × 10⁴
What does a negative exponent mean?
A negative exponent indicates a number less than 1 (a decimal). 10⁻³ means 1/10³ = 1/1000 = 0.001. So 2.3 × 10⁻⁴ means 2.3 divided by 10000, which equals 0.00023.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. For example: (2 × 10³) × (3 × 10⁴) = (2 × 3) × 10³⁺⁴ = 6 × 10⁷. This is one reason scientific notation is so useful for calculations.
Can the coefficient be negative?
Yes! Negative numbers can be expressed in scientific notation. For example, -4.5 × 10⁴ = -45000. The negative sign applies to the entire number, not just the coefficient.
Is 10 × 10³ proper scientific notation?
No. In proper scientific notation, the coefficient must be between 1 and 10. So 10 × 10³ should be written as 1 × 10⁴ (or simply 10⁴). Our calculator always outputs proper scientific notation.
Why use a scientific notation calculator?
A scientific notation calculator saves time, prevents errors, and shows step-by-step conversions. It's perfect for homework, science classes, engineering calculations, or any work involving very large or very small numbers.
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Educational Disclaimer
This calculator is provided for educational purposes and homework assistance. While we strive for accuracy, please verify critical calculations independently. Results should not be used as the sole basis for important financial, academic, or professional decisions. Always check your work and consult with appropriate professionals when needed.