## Significant Digits in Calculations When performing **math with measured values**, your final answer should reflect the **same level of precision** as the **least precise measurement** used in the calculation. There are two main categories of operations with different rules: - **Addition and Subtraction** - **Multiplication and Division** ## Addition and Subtraction: Use Decimal Places For **addition or subtraction**, the final answer should be rounded to the **same number of decimal places** as the **value with the fewest decimal places**. ### Example 1 $ 4.62 + 1.3 = 5.92 \Rightarrow \text{round to 1 decimal place} \Rightarrow \boxed{5.9} $ Explanation: - $4.62$ has 2 decimal places - $1.3$ has 1 decimal place → round answer to **1 decimal place** ### Example 2 $ 12.05 - 3.112 = 8.938 \Rightarrow \text{round to 2 decimal places} \Rightarrow \boxed{8.94} $ Explanation: - $12.05$ has 2 decimal places - $3.112$ has 3 decimal places → round to **2 decimal places** ## Multiplication and Division: Use Significant Figures For **multiplication or division**, the final answer should have the **same number of significant digits** as the **input with the fewest significant digits**. ### Example 3 $ 2.5 \times 3.42 = 8.55 \Rightarrow \text{round to 2 sig figs} \Rightarrow \boxed{8.6} $ Explanation: - $2.5$ has 2 sig figs - $3.42$ has 3 sig figs → answer must have **2 sig figs** ### Example 4 $ 7.630 \div 2.0 = 3.815 \Rightarrow \text{round to 2 sig figs} \Rightarrow \boxed{3.8} $ Explanation: - $7.630$ has 4 sig figs - $2.0$ has 2 sig figs → answer must have **2 sig figs** ## How This Applies in Electrical Testing **Example: Calculating Resistance with Ohm’s Law** $ R = \frac{V}{I} $ If: - $V = 12.0$ V (3 sig figs) - $I = 3.0$ A (2 sig figs) Then: $ R = \frac{12.0}{3.0} = 4.0\ \Omega \ (\text{2 sig figs}) $ Even if your calculator shows 4.000000, you **must round to 2 significant digits**. ## When Mixing Operations If a calculation involves both types of operations, **do the steps in order**, keeping track of significant digits or decimal places at each stage. **Example:** $ (12.5 - 3.2) \div 4.00 $ Step 1: Subtraction $ 12.5 - 3.2 = 9.3 \ (\text{rounded to 1 decimal place}) $ Step 2: Division $ 9.3 \div 4.00 = 2.325 \Rightarrow \text{round to 3 sig figs} \Rightarrow \boxed{2.33} $ ## Summary |Operation Type|Rule| |---|---| |Addition / Subtraction|Round final answer to the **fewest decimal places**| |Multiplication / Division|Round final answer to the **fewest significant digits**| Being consistent with these rules helps ensure your test reports, lab calculations, and documentation are **scientifically valid** and **technically credible**.