Scientific Notation Calculator
Convert between standard and scientific notation with detailed analysis
Notation Conversion
Conversion Results
Enter a number to convert between notations
Understanding Scientific Notation
What is Scientific Notation?
Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It's commonly used in science, engineering, and mathematics to represent very large or very small quantities.
Format:
a × 10^n where 1 ≤ |a| < 10 and n is an integer
Example: 3.45 × 10^6 = 3,450,000
Why Use Scientific Notation?
Scientific notation provides a standardized way to represent numbers across different scales, making it easier to work with very large or very small quantities in calculations and comparisons.
- •Clarity: Reduces ambiguity in large numbers
- •Efficiency: Compact representation of extreme values
- •Calculation: Easier multiplication and division
- •Comparison: Easy to compare orders of magnitude
Conversion Rules
To Scientific Notation:
1. Move decimal point to create a number between 1 and 10
2. Count how many places you moved the decimal
3. Use this count as the exponent (positive for large numbers, negative for small numbers)
From Scientific Notation:
1. Multiply the mantissa by 10 raised to the exponent
2. Move the decimal point by the exponent places
3. Add zeros if needed for the correct magnitude
Common Examples
Large Numbers
Small Numbers
Real-World Applications
Physics
Fundamental constants
- • Speed of light
- • Gravitational constant
- • Planck's constant
- • Elementary charge
Chemistry
Molecular quantities
- • Avogadro's number
- • Atomic masses
- • Concentration units
- • Reaction rates
Astronomy
Cosmic scales
- • Stellar distances
- • Galaxy masses
- • Planetary orbits
- • Light years
Engineering
Technical specifications
- • Material properties
- • Electrical values
- • Tolerances
- • Frequencies
Biology
Biological scales
- • Cell sizes
- • DNA molecules
- • Population counts
- • Microscopic measurements
Computer Science
Digital quantities
- • Data storage
- • Processing speeds
- • Network bandwidth
- • Memory capacity
Engineering Notation
Engineering Notation vs Scientific Notation
Engineering notation is similar to scientific notation but uses exponents that are multiples of 3, making it easier to work with SI prefixes.
Scientific: 1.23 × 10^4
Exponent can be any integer
Engineering: 12.3 × 10^3
Exponent is multiple of 3
SI Prefixes:
10^-12 (pico), 10^-9 (nano), 10^-6 (micro), 10^-3 (milli), 10^3 (kilo), 10^6 (mega), 10^9 (giga), 10^12 (tera)