Math Tools
Scientific Notation Converter
Convert numbers to and from scientific notation (exponential form). Handle very large and very small numbers with E-notation. Perfect for scientists, engineers, and students.
Use Scientific Notation Converter to get instant results without uploads or sign-ups. Everything runs securely in your browser for fast, reliable output.
Your results will appear here.
About this tool
Scientific notation (also called standard form or exponential notation) is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It's expressed as a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer. For example: 6,020,000,000,000,000,000,000,000 (Avogadro's number) = 6.02 × 10²³. In E-notation (computer format), this becomes 6.02e23 or 6.02E+23.
Scientific notation is essential in science, engineering, and mathematics for working with extreme values. It simplifies calculations, reduces errors from counting zeros, maintains precision by showing significant figures clearly, and makes very large or small numbers readable. Scientists use it for atomic scales (0.000000001 m = 1 × 10⁻⁹ m), astronomical distances (9.461 × 10¹⁵ m = 1 light-year), and molecular quantities.
Our converter handles both directions: standard numbers to scientific notation and scientific notation back to standard form. It supports multiple input formats including E-notation (1.5e-8), standard scientific notation with × (1.5 × 10⁻⁸), and plain numbers. The tool automatically detects your input type and provides comprehensive output including coefficient, exponent, word form, and order of magnitude.
Understanding scientific notation helps with: chemistry calculations (molar masses, concentrations), physics problems (speeds, distances, energies), engineering (very small tolerances, very large forces), astronomy (planetary distances, star masses), computer science (large data sizes, computational complexity), and any field dealing with extreme numerical ranges. It's a fundamental skill for STEM education.
Usage examples
Large Number to Scientific
Speed of light in meters/second
Input: 299792458 Output: 2.99792458 × 10⁸ (or 2.99792458e8) Meaning: 2.99... followed by 8 more digits
Small Number to Scientific
Electron mass in kilograms
Input: 0.00000000000000000000000000000091093837 Output: 9.1093837 × 10⁻³¹ Meaning: 9.1... preceded by 31 zeros
E-notation to Standard
Convert computer format
Input: 6.02e23 Output: 602,000,000,000,000,000,000,000 Meaning: Avogadro's number
Negative Exponent
Wavelength of visible light
Input: 5.5e-7 Output: 0.00000055 (550 nanometers) Meaning: 550 nm = 5.5 × 10⁻⁷ m
Very Large Number
Number of atoms in the universe
Input: 1e80 Output: 1 × 10⁸⁰ (1 followed by 80 zeros) Estimated atoms in observable universe
How to use
- Enter a number in standard form (e.g., 12300000) or scientific notation (e.g., 1.23e7)
- Select conversion mode: Auto-detect, To Scientific, or From Scientific
- The tool automatically converts and shows multiple representations
- View coefficient, exponent, and equivalent forms
- Copy the result for use in calculations or reports
- Perfect for handling extremely large or small numbers
Benefits
- Convert between standard and scientific notation instantly
- Auto-detect input format (standard, E-notation, or scientific)
- Handle extremely large numbers (up to 10³⁰⁸)
- Handle extremely small numbers (down to 10⁻³⁰⁸)
- Show coefficient and exponent separately
- Display in multiple formats (standard, E-notation, × notation)
- Preserve significant figures correctly
- Show order of magnitude and scale
- Provide word representation (millions, billions, etc.)
- Educational: explains the conversion process
- Essential for chemistry, physics, and engineering
- Works with negative numbers and negative exponents
FAQs
What is scientific notation?
Scientific notation expresses numbers as a × 10ⁿ where a (coefficient) is between 1 and 10, and n (exponent) is an integer. For example: 5,300 = 5.3 × 10³. This format is compact, highlights significant figures, and simplifies calculations. Positive exponents (10³) mean large numbers, negative exponents (10⁻³) mean small numbers. It's the standard way scientists write extreme values.
What is E-notation and how is it different?
E-notation is computer/calculator format for scientific notation. Instead of 2.5 × 10⁶, computers write 2.5e6 or 2.5E+06. The "e" means "times 10 to the power of". They're mathematically identical: 3.2e-5 = 3.2 × 10⁻⁵ = 0.000032. E-notation is easier to type and display on screens. Scientific calculators and programming languages use E-notation.
When should I use scientific notation?
Use scientific notation for: very large numbers (0.000000001 becomes 1 × 10⁻⁹), very small numbers (8,500,000,000 becomes 8.5 × 10⁹), numbers with many zeros (easier to write and less error-prone), when precision matters (shows significant figures clearly), and in scientific calculations where numbers span many orders of magnitude. It's essential in chemistry, physics, astronomy, and engineering.
How do I read the exponent?
Positive exponent (10⁵) = move decimal 5 places right (multiply by 10 five times). 2 × 10³ = 2,000. Negative exponent (10⁻⁴) = move decimal 4 places left (divide by 10 four times). 5 × 10⁻² = 0.05. The exponent tells you how many zeros and which direction. Large positive = big number, large negative = small number.
What are significant figures in scientific notation?
Scientific notation clearly shows significant figures—the meaningful digits in a number. In 2.50 × 10⁴, there are 3 significant figures (2, 5, 0). The coefficient contains all significant figures, while the exponent just indicates magnitude. This helps maintain precision in calculations and shows measurement accuracy. For example, 25,000 could be 2 or 5 sig figs, but 2.5 × 10⁴ (2 sig figs) vs 2.5000 × 10⁴ (5 sig figs) is unambiguous.
How do I multiply or divide numbers in scientific notation?
Multiply: multiply coefficients, add exponents. (2 × 10³) × (3 × 10⁴) = 6 × 10⁷. Divide: divide coefficients, subtract exponents. (8 × 10⁶) ÷ (2 × 10²) = 4 × 10⁴. Then adjust if coefficient is outside 1-10 range. For adding/subtracting, exponents must match first, then add/subtract coefficients. Scientific notation makes these operations much easier than working with full numbers.
What's the difference between 1e10 and 1e-10?
1e10 = 1 × 10¹⁰ = 10,000,000,000 (ten billion, very large). 1e-10 = 1 × 10⁻¹⁰ = 0.0000000001 (one ten-billionth, very small). The negative exponent makes it a tiny fraction. Remember: positive exponent = big number, negative exponent = small number. The magnitude is the same (10), but the sign determines direction on the number line.
Can scientific notation represent zero?
Technically, 0 cannot be expressed in true scientific notation (which requires 1 ≤ |a| < 10). However, calculators often display 0 as 0e0 or 0 × 10⁰. Mathematically, any number times zero equals zero, so 0 × 10ⁿ = 0 for any n. In practice, just write zero as 0—scientific notation isn't necessary or meaningful for zero.
Related tools
View all toolsFibonacci Calculator
Calculate Fibonacci sequence numbers, find the Nth Fibonacci number, generate sequences, and explore the golden ratio. Perfect for mathematics, nature patterns, and programming.
Math ToolsFraction Calculator
Calculate fractions: add, subtract, multiply, divide. Simplify fractions, convert to decimals, and find common denominators.
Math ToolsGolden Ratio Calculator
Calculate golden ratio (φ = 1.618) proportions for design, art, and architecture. Find harmonious dimensions using the divine proportion.
Math Tools