Scientific Notation Calculator - Convert & Calculate
Convert numbers to scientific notation and perform arithmetic operations with instant, accurate results
Scientific Notation Calculator
Result
What is a Scientific Notation Calculator?
A Scientific Notation Calculator is a free mathematical tool that converts numbers to and from scientific notation (a × 10^n format) and performs arithmetic operations on numbers in scientific notation. It's essential for working with very large or very small numbers in science, engineering, and mathematics.
This calculator is perfect for:
- Students - Learn and verify scientific notation conversions for homework
- Scientists & Engineers - Work with measurements spanning multiple orders of magnitude
- Data Analysts - Handle extremely large datasets and statistical values
For basic mathematical operations and calculations, check out our Scientific Calculator to perform advanced mathematical functions.
To calculate powers and exponents, explore our Exponent Calculator to compute exponential expressions quickly.
For working with logarithms, use our Log Calculator to calculate logarithms in different bases.
To find roots of numbers, try our Root Calculator to compute square roots, cube roots, and nth roots.
How Scientific Notation Works
Scientific notation represents numbers in the form:
Where:
- a = coefficient (1 ≤ |a| < 10)
- n = exponent (integer)
Key Concepts
Coefficient
The number between 1 and 10. Always has one non-zero digit before the decimal point.
Exponent
The power of 10. Positive for large numbers, negative for small numbers.
E-notation
Computer format: 4.5E4 means 4.5 × 10^4. Common in calculators and programming.
Order of Magnitude
The exponent indicates the scale: 10^3 (thousands), 10^6 (millions), 10^9 (billions).
How to Use This Calculator
Choose Mode
Select Convert or Calculate mode
Enter Value(s)
Type number or scientific notation
Select Operation
Choose +, -, ×, or ÷ (calculate mode)
View Results
Get scientific notation and decimal form
Benefits of Using This Calculator
- • Instant Conversion: Convert between standard and scientific notation instantly.
- • Accurate Calculations: Perform arithmetic operations without losing precision.
- • Multiple Formats: See results in scientific notation, E-notation, and decimal form.
- • Learning Tool: Understand the relationship between different number representations.
- • Professional Use: Essential for scientific research, engineering, and data analysis.
Operation Rules
1. Addition/Subtraction
Convert to same exponent, then add/subtract coefficients. Example: (2×10^3) + (5×10^2) = (2×10^3) + (0.5×10^3) = 2.5×10^3
2. Multiplication
Multiply coefficients, add exponents. Example: (2×10^3) × (3×10^4) = 6×10^7
3. Division
Divide coefficients, subtract exponents. Example: (6×10^5) ÷ (2×10^2) = 3×10^3
4. Coefficient Range
Results are normalized so 1 ≤ |coefficient| < 10 for proper scientific notation.
Frequently Asked Questions (FAQ)
Q: What is scientific notation?
A: Scientific notation is a way of expressing very large or very small numbers in the form a × 10^n, where 1 ≤ |a| < 10 and n is an integer. For example, 5,000,000 = 5 × 10^6 and 0.00003 = 3 × 10^-5.
Q: How do I convert a number to scientific notation?
A: Move the decimal point to create a number between 1 and 10. Count how many places you moved it. If you moved left, the exponent is positive. If you moved right, the exponent is negative. For example, 45000 becomes 4.5 × 10^4.
Q: Can this calculator perform operations in scientific notation?
A: Yes! This calculator can add, subtract, multiply, and divide numbers in scientific notation. It handles all calculations and displays results in proper scientific notation format.
Q: What is E-notation?
A: E-notation is a computer-friendly way to write scientific notation. Instead of 3 × 10^5, you write 3E5 or 3e5. The E means 'times 10 to the power of'. It's commonly used in calculators and programming.