Exponential Notation Calculator

Convert numbers to and from exponential (E) notation with step-by-step explanations

Number Converter

Accepts standard decimal numbers (123.45) or exponential notation (1.23e5)

Number of significant digits to display

Standard

Detected format of your input

Conversion Results

E Notation

1.23e+5

Exponential notation using 'e' to represent ×10

Scientific Notation

1.23 × 10⁺5

Standard scientific notation with multiplication symbol

Standard Notation

123456

Regular decimal number format

Number Breakdown

Mantissa:

1.23

Exponent:

5

Step-by-Step Conversion

1

1. Starting number: 123456

2

2. Move decimal point 5 places to the left

3

3. Mantissa: 1.23

4

4. Exponent: +5 (positive because we moved left)

5

5. Result: 1.23 × 10⁺5

6

6. E notation: 1.23e+5

Try These Examples

Quick Reference

E Notation Format

±M.MMe±EE

M = mantissa digits, E = exponent

Examples

1000 = 1.0e+3

0.001 = 1.0e-3

123.45 = 1.23e+2

0.00678 = 6.78e-3

Rules

  • • Mantissa: 1 ≤ |M| < 10
  • • Positive exponent: number ≥ 10
  • • Negative exponent: number < 1
  • • Zero exponent: 1 ≤ number < 10

Common Applications

Scientific Research

Representing very large or small measurements

Programming

Computer calculations and data storage

Engineering

Calculations with extreme values

Understanding Exponential Notation

What is Exponential Notation?

Exponential notation, also known as E notation or scientific notation, is a way to express very large or very small numbers in a compact, standardized format. It uses the letter 'e' (or 'E') to represent "times 10 to the power of".

Format Structure

M.MMM e ±EE

  • M.MMM: Mantissa (1 ≤ |M| < 10)
  • e: Exponential indicator
  • ±EE: Exponent (power of 10)

Conversion Rules

  • For numbers ≥ 10: Move decimal left, positive exponent
  • For numbers < 1: Move decimal right, negative exponent
  • For 1 ≤ number < 10: No movement, zero exponent

Real-World Examples

Speed of Light

299,792,458 m/s = 2.998e+8 m/s

Avogadro's Number

602,214,076,000,000,000,000,000 = 6.022e+23

Electron Mass

0.000000000000000000000000000000910938 kg = 9.109e-31 kg

Benefits

  • Compact representation of extreme values
  • Easy comparison of magnitudes
  • Standard format across scientific fields
  • Prevents calculation errors with many zeros