Significant Figures & Dimensional Analysis

1.8: Handling Numbers Rules: Determining Sig Figs

Sig fig Examples:

• 2021 – 4
• 2020 – 3
• \(1.60 \times 10^{-19}\) – 3
• \(6.022 \times 10^{23}\) – 4
• 7500 – 2
• 750 – 2
• 750. – 3
• 0.750 – 3

Precision Examples (always choose the last sig fig):

• 2021 – one’s place
• 2020 – ten’s place
• \(1.60 \times 10^{-19}\) – \(10^{-21}\)’st place
• \(6.022 \times 10^{23}\) – \(10^{20}\)’st place
• 7500 – hundred’s place
• 750 – ten’s place
• 750. – one’s place
• 0.750 – thousandth’s place

Addition and Subtraction and Sig figs

Multiplication and Division Rule: min(num1.sig_figs, num2.sig_figs)

Addition and Subtraction Rule: min(num1.decimal_places, num2.decimal_places) [Choose the least precise]

Addition Subtraction Examples:

• \(56.78 - 0.876 = 55.90\)
• \(14.023 + 29.0034 + 0.11 = 43.14\)
• \(14.023 + 29.0034 + 0.1100 = 43.136\)
• \(75 + 110 + 83 = 270\)
• \(620 + 530 + 450 = 1.60 \times 10^{3}\)

In general, your measurements limit the output sig figs

1.9: Unit Conversion

Dimensional Analysis

\[ \frac{1.27\text{ kg}}{} \times \frac{2.205\text{ lbs}}{\text{kg}} = 2.80\text{ lbs} \]

\[ \frac{5.0\text{ km}}{} \times \frac{1\text{ mile}}{1.61\text{ km}} = 3.1\text{ miles} \]

1 mL = 1 \(\text{cm}^{3}\)

\[ \frac{2.014698447 \text{ cm}^{3}}{} \times \frac{1 \text{ mL}}{1 \text{ cm}^{3}} \times \frac{1\text{ oz}}{29.5735\text{ mL}} = 0.06813\text{ oz} \]

Notice how the 3 in the following example does not affect the final number of significant figures

\[ \frac{109.4\text{ yards}}{} \times \frac{3 \text{ feet}}{1 \text{ yards}} = 328.2\text{ feet} \]