Scientific Notation Calculator
Convert numbers to and from scientific notation (exponential form). Perform arithmetic operations and learn about powers of 10 with step-by-step explanations.
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Scientific Notation Explained
What is Scientific Notation?
Scientific notation is a way of expressing very large or very small numbers in a compact form. It's written as a × 10n, where 'a' is a number between 1 and 10 (called the coefficient or mantissa), and 'n' is an integer (called the exponent).
Where: 1 ≤ |a| < 10 and n is an integer
Converting to Scientific Notation
To convert a number to scientific notation:
- Move the decimal point to create a number between 1 and 10
- Count how many places you moved the decimal point
- If you moved left, the exponent is positive; if right, it's negative
- Write in the form a × 10n
Examples
How to Use This Calculator
Applications of Scientific Notation
Science & Engineering
- Expressing astronomical distances (light-years, parsecs)
- Atomic and molecular measurements
- Electrical engineering calculations
- Chemical concentrations and reactions
- Physics constants and measurements
- Computer science and data storage
Real-World Examples
- Speed of light: 3.0 × 108 m/s
- Avogadro's number: 6.022 × 1023
- Planck constant: 6.626 × 10-34 J⋅s
- Mass of an electron: 9.109 × 10-31 kg
- Distance to nearest star: 4.24 × 1016 m
- Size of a virus: 1.0 × 10-7 m
Example Calculations
Example 1: Converting Large Numbers
Example 2: Converting Small Numbers
Example 3: Multiplication in Scientific Notation
Frequently Asked Questions
What's the difference between scientific and engineering notation?
Scientific notation uses exponents that can be any integer, while engineering notation uses exponents that are multiples of 3 (like 10³, 10⁶, 10⁹). This aligns with common engineering prefixes like kilo-, mega-, giga-, etc.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents: (a × 10ᵐ) × (b × 10ⁿ) = (a × b) × 10^(m+n). If the result's coefficient is not between 1 and 10, adjust it accordingly.
When should I use scientific notation?
Scientific notation is most useful for very large numbers (like astronomical distances) or very small numbers (like atomic measurements). It makes calculations easier and reduces the chance of errors when dealing with many zeros.