## Operations with Scientific Notation In electrical work, you often need to **multiply**, **divide**, **add**, or **subtract** numbers in scientific notation. This lesson shows how to do these operations quickly and correctly. ### Multiplication Use this rule: $(a \times 10^m) \cdot (b \times 10^n) = (a \cdot b) \times 10^{m+n}$ **Example:** $(3.0 \times 10^2) \cdot (2.0 \times 10^4) = 6.0 \times 10^6$ ### Division Use this rule: $\frac{a \times 10^m}{b \times 10^n} = \left(\frac{a}{b}\right) \times 10^{m-n}$ **Example:** $\frac{6.0 \times 10^5}{2.0 \times 10^2} = 3.0 \times 10^3$ ### Addition and Subtraction (Same Exponent Only) To add or subtract, the exponents **must be the same**. **Example:** $(3.5 \times 10^4) + (2.5 \times 10^4) = (3.5 + 2.5) \times 10^4 = 6.0 \times 10^4$ If the exponents are **not the same**, adjust one number: **Example:** $(5.0 \times 10^3) + (2.0 \times 10^2)$ Convert $2.0 \times 10^2$ to the same exponent: $2.0 \times 10^2 = 0.2 \times 10^3$ Now add: $5.0 \times 10^3 + 0.2 \times 10^3 = 5.2 \times 10^3$ ### Electrical Examples **Power Calculation:** $P = V \cdot I = (1.2 \times 10^3)\ \text{V} \cdot (2.5 \times 10^{-3})\ \text{A}$ Multiply: $1.2 \cdot 2.5 = 3.0 \quad \text{and} \quad 10^3 \cdot 10^{-3} = 10^0 = 1$ Answer: $3.0 \times 10^0 = 3.0\ \text{W}$ ### Tips for Operations - When **multiplying/dividing**, just use exponent rules - When **adding/subtracting**, match exponents first - Use calculators in **scientific mode** when available - Watch your significant digits and rounding ### Summary - Multiply: add exponents - Divide: subtract exponents - Add/Subtract: match exponents first - These skills help with power formulas, conversions, and reading meters