Lesson 13-9: Perform Operations with Numbers in Scientific Notation

Property

To multiply and divide numbers in scientific notation, group the coefficients together and group the powers of 10 together, then use the Properties of Exponents.

• Multiplication: Multiply the decimal coefficients and ADD the exponents.

• Division: Divide the decimal coefficients and SUBTRACT the exponents.

Property

After performing an operation, your result might not be in the proper scientific notation format, which is written as:

(where $1 \leq c < 10$ and $n$ is an integer)

Property

To add numbers in scientific notation, first ensure they have the same power of 10. Then, add the decimal factors and keep the common power of 10. The general rule is $(a \times 10^n) + (b \times 10^n) = (a + b) \times 10^n$.

Examples

• Same powers: $(4.2 \times 10^5) + (3.5 \times 10^5) = (4.2 + 3.5) \times 10^5 = 7.7 \times 10^5$
• Different powers: $(6.1 \times 10^3) + (2.5 \times 10^4) = (0.61 \times 10^4) + (2.5 \times 10^4) = (0.61 + 2.5) \times 10^4 = 3.11 \times 10^4$

Explanation

When adding numbers in scientific notation, the exponents must be the same. If they are already the same, you can simply add the decimal parts and keep the common power of 10. If the exponents are different, you must first rewrite one of the numbers so that its exponent matches the other. Finally, ensure your answer is written in proper scientific notation.