C

Scientific Notation Converter

Convert between decimal and scientific notation instantly. Perfect for students, scientists, and engineers working with very large or very small numbers.

Scientific Notation Converter

Convert between decimal and scientific notation formats

Input Format
Coefficient (1 ≤ coefficient < 10)
Exponent (power of 10)

Conversion Results

Decimal Format

1,000,000

Scientific Notation

1 × 10^6

Coefficient

1

Exponent

6

Scale Category

Moderate Scale: Engineering and scientific measurements

Scientific Notation Scale Categories

Large Numbers (Positive Exponents)

10³ to 10⁶1,000 - 1,000,000

Common scale measurements

  • • Population counts
  • • Distance measurements
  • • Economic values
10⁶ to 10⁹1M - 1B

Large scale measurements

  • • Astronomical distances
  • • Computer memory
  • • Population of countries
10⁹+1B+

Astronomical scales

  • • Interstellar distances
  • • Avogadro's number
  • • Universal constants

Small Numbers (Negative Exponents)

10⁻³ to 10⁻⁶0.001 - 0.000001

Precise measurements

  • • Millimeter measurements
  • • Financial precision
  • • Engineering tolerances
10⁻⁶ to 10⁻⁹1μ - 1n

Microscopic scale

  • • Cell dimensions
  • • Wavelength of light
  • • Molecular sizes
10⁻⁹+1n+

Atomic/subatomic scale

  • • Atomic radii
  • • Planck length
  • • Quantum measurements

How to Convert to Scientific Notation

Scientific Notation Format

General Form: a × 10ⁿ
Where: 1 ≤ |a| < 10 and n is an integer
Examples: 1.23 × 10⁵, -4.56 × 10⁻³

Conversion Steps:

  1. 1
    Identify the decimal point location
    Find where the decimal point currently is in your number
  2. 2
    Move decimal to create coefficient
    Move decimal so only one non-zero digit is to its left
  3. 3
    Count the moves for exponent
    Number of places moved = exponent (positive if moved left, negative if moved right)
  4. 4
    Write in scientific notation
    Format as: coefficient × 10^exponent

Important Considerations

⚠️ Precision Warning

Very large or very small numbers may lose precision due to floating-point limitations.

🔢 Coefficient Rules

Coefficient must be between 1 and 10 (exclusive of 10)

  • • 1 ≤ |coefficient| < 10
  • • Can be positive or negative
  • • Only one digit before decimal
📐 Exponent Rules

Exponent must be an integer (whole number)

  • • Can be positive, negative, or zero
  • • Represents power of 10
  • • Shows decimal place movement
🎯 Common Formats

Multiple ways to write scientific notation

  • • 1.23 × 10⁵ (standard)
  • • 1.23e+5 (computer)
  • • 1.23E+5 (alternative)
⚡ Zero Handling

Special case for zero values

  • • Zero = 0 (no scientific notation)
  • • No coefficient or exponent needed
  • • Simplest representation

Example Cases

Case 1: Large Number Conversion

Input: 1,200,000
Process: Move decimal 6 places left
Result: 1.2 × 10⁶
Use Case: Population data
Real Example: City population
Benefit: Easier to read and compare

Application: Perfect for scientific papers, engineering calculations, and data analysis where large numbers are common.

Case 2: Small Number Conversion

Input: 0.000000123
Process: Move decimal 7 places right
Result: 1.23 × 10⁻⁷
Use Case: Microscopic measurements
Real Example: Wavelength of light
Benefit: Clear magnitude indication

Application: Essential for physics, chemistry, and biology where precise measurements of very small quantities are required.

Common Scientific Notation Reference Values

Planck Length1.616255e-35

Smallest meaningful length in physics

Electron Radius2.817940e-15

Classical electron radius

Hydrogen Atom5.290000e-11

Bohr radius of hydrogen atom

DNA Helix2.000000e-9

Diameter of DNA double helix

Red Blood Cell7.000000e-6

Diameter of human red blood cell

Grain of Sand5.000000e-4

Typical sand grain diameter

Human Hair8.000000e-5

Average human hair diameter

Paper Thickness1.000000e-4

Standard paper thickness

Meter1

SI base unit of length

Football Field100

Length of American football field

Mount Everest8,848

Height of Mount Everest

Earth Diameter1.274200e+7

Earth diameter at equator

Sun Diameter1.392700e+9

Sun diameter

Light Year9.461000e+15

Distance light travels in one year

Universe Age4.320000e+17

Age of universe in seconds

Source: National Institute of Standards and Technology (NIST) and International System of Units (SI)

Related Calculators

Frequently Asked Questions

What is scientific notation and why is it important?
Scientific notation is a way of writing very large or very small numbers using powers of 10. It's essential in science, engineering, and mathematics because it makes calculations with extreme values manageable and reduces errors. For example, 6.022 × 10²³ (Avogadro's number) is much clearer than 602,200,000,000,000,000,000,000.
How do I convert a decimal number to scientific notation?
To convert to scientific notation: 1) Move the decimal point so there's one non-zero digit to its left, 2) Count how many places you moved it, 3) Write the number as coefficient × 10^exponent. For example, 1,200,000 becomes 1.2 × 10⁶ (moved 6 places right).
What's the difference between coefficient and mantissa?
In scientific notation, the coefficient (also called mantissa) is the number between 1 and 10 that multiplies the power of 10. For 3.14 × 10⁵, the coefficient is 3.14. The coefficient must always be ≥1 and <10 for proper scientific notation format.
Can I use this converter for negative numbers?
Yes! The converter handles negative numbers correctly. For example, -0.000123 becomes -1.23 × 10⁻⁴. The negative sign applies to the entire number, while the exponent can be positive or negative independently.
What's the precision limit of this converter?
This converter supports up to ~15 significant digits, consistent with typical double-precision floating-point. This ensures accurate conversions for most scientific calculations while maintaining computational efficiency.
Scientific Notation Converter