Scientific Notation Calculator
Convert numbers to and from scientific notation (a * 10^b). Supports standard numbers, E notation, and scientific notation input.
What is scientific notation and why is it used?
Scientific notation expresses numbers as a * 10^b where 1 <= |a| < 10 and b is an integer. Used for very large or small numbers. Examples: 300,000,000 = 3 * 10^8 (speed of light m/s), 0.0000000016 = 1.6 * 10^-9 (nanometer). Benefits: Compact representation, easier calculations, clearer magnitude comparison. Essential in: Physics, chemistry, astronomy, engineering. Makes 602,000,000,000,000,000,000,000 (Avogadro's number) → 6.02 * 10^23.
How do I convert a number to scientific notation?
Steps: 1) Move decimal point until one non-zero digit remains to the left. 2) Count moves (exponent). 3) Moving left = positive exponent, right = negative. Examples: 4,500 → 4.5 * 10^3 (moved left 3 places). 0.0067 → 6.7 * 10^-3 (moved right 3 places). 1.23 → 1.23 * 10^0 (no move). Coefficient must be >=1 and <10. For negative numbers, keep sign with coefficient: -4500 = -4.5 * 10^3.
How do I convert from scientific notation to standard form?
Move decimal point based on exponent. Positive exponent: Move right (number gets larger). Negative exponent: Move left (number gets smaller). Examples: 5.3 * 10^4 → 53,000 (move right 4 places). 2.1 * 10^-3 → 0.0021 (move left 3 places). 7.89 * 10^0 → 7.89 (no move). Add zeros as placeholders when needed. 3 * 10^6 = 3,000,000 (6 zeros added).
What is E notation in calculators?
E notation is calculator/computer shorthand for scientific notation. Format: aEb means a * 10^b. Examples: 3E8 = 3 * 10^8 = 300,000,000. 1.5E-4 = 1.5 * 10^-4 = 0.00015. 6.02E23 = 6.02 * 10^23 (Avogadro's number). Used in: Excel, programming, calculator displays. Same concept, different symbol. No spaces, capital E. Negative exponents use E-: 2E-5 = 0.00002.
How do I multiply and divide numbers in scientific notation?
Multiplication: (a * 10^m) * (b * 10^n) = (a * b) * 10^(m+n). Example: (2 * 10^3) * (3 * 10^4) = 6 * 10^7. Division: (a * 10^m) / (b * 10^n) = (a / b) * 10^(m-n). Example: (8 * 10^5) / (2 * 10^3) = 4 * 10^2. Adjust if coefficient outside [1,10): 15 * 10^4 = 1.5 * 10^5. Addition/Subtraction: Match exponents first, then add/subtract coefficients.