Arithmetic with Scientific Notation
Performing calculations with numbers in scientific notation follows specific rules depending on the operation. Understanding these rules is essential for working efficiently with very large or very small numbers.
Rules by Operation
Multiplication
Multiply the coefficients and add the exponents.
(a1 × 10^n1)(a2 × 10^n2) = (a1·a2) × 10^(n1+n2)
Division
Divide the coefficients and subtract the exponents.
(a1 × 10^n1)/(a2 × 10^n2) = (a1/a2) × 10^(n1-n2)
Addition & Subtraction
First match the exponents, then add or subtract the coefficients.
Match exponents first, then add/subtract coefficients
Important Notes
- After any operation, normalize the result so the coefficient is between 1 and 10.
- For addition and subtraction, you must first convert both numbers to the same power of 10.
- Multiplication and division are generally simpler since you work with coefficients and exponents separately.
- Always check your result by converting back to standard notation to verify.