Addition and Subtraction in Scientific Notation

Introduction to Scientific Notation Operations

Scientific notation is a method used to express very large or very small numbers in the form A × 10n, where A is a coefficient and n is an integer exponent. When performing addition or subtraction with numbers in scientific notation, it is essential to follow specific rules to ensure accuracy.

Rules for Addition and Subtraction

• Exponents Must Match: Only numbers with the same exponent can be directly added or subtracted. The coefficients are added or subtracted, while the exponent remains unchanged.

• Adjusting Exponents: If the exponents are not the same, convert one or both numbers so that their exponents match. This is done by shifting the decimal point in the coefficient and adjusting the exponent accordingly.

• Significant Figures: The final answer should be rounded to the least number of decimal places present in the original numbers after aligning exponents.

General Formulas

• Subtraction:

  • Given and :

• Addition:

  • Given and :

Steps for Adding or Subtracting in Scientific Notation

1. Check if the exponents are the same.

2. If not, convert one number so that both exponents match (use the smaller exponent as the common value).

3. Add or subtract the coefficients.

4. Keep the common exponent unchanged.

5. Round the answer to the least number of decimal places from the original numbers.

Examples

Example 1

Problem:

• First, convert to so both numbers have the same exponent.

• Add the coefficients:

• Result:

• Adjust to proper scientific notation:

• Note: The answer is rounded to the least number of decimal places (here, 2 decimal places).

Example 2

Problem:

• Convert all terms to the same exponent, :

• Subtract the coefficients:

• Result: (rounded to 3 significant figures)

Summary Table: Steps for Addition/Subtraction in Scientific Notation

Key Terms

• Scientific Notation: A way of expressing numbers as a product of a coefficient and a power of ten.

• Exponent: The power of ten in scientific notation.

• Coefficient: The number multiplied by the power of ten.

• Significant Figures: The digits in a number that carry meaning contributing to its precision.