Calculations Using Sig Figs
Rounding
• Some of us are used to always rounding 5s up
• E.g. 20.5  21
• In Chem 11, we will round 5s to the nearest even number
• E.g. 20.5  20 (20 is nearer than 22)
• E.g. 21.5  22 (22 is nearer than 20)
Multiplication & Division
• Round the answer to the least number of sig figs contained in the
question
• 2.391 x 4.5 = ?
Multiplication & Division
• 2.391 x 4.5 = ?
• 4 sig figs x 2 sig figs = ?
• 4 sig figs x 2 sig figs = 2 sig figs
• 2.391 x 4.5 = 10.7595
Multiplication & Division
• 2.391 x 4.5 = ?
• 4 sig figs x 2 sig figs = ?
• 4 sig figs x 2 sig figs = 2 sig figs
• 2.391 x 4.5 = 10.7595  11 (2 sig figs)
Multiplication & Division
• Practice: Hebden p.39 #56
Addition & Subtraction
• Round off the answer to the least precise number in the problem
• Remember that least precise means fewest decimal places
Addition & Subtraction
• 29.347 + 2.33 = ?
• 3 decimals + 2 decimals = ?
Addition & Subtraction
• 29.347 + 2.33 = ?
• 3 decimals + 2 decimals = 2 decimals
Addition & Subtraction
• 29.347 + 2.33 = ?
• 3 decimals + 2 decimals = 2 decimals
• 29.347 + 2.33 = 31.677  round to 2 decimals
Addition & Subtraction
• 29.347 + 2.33 = ?
• 3 decimals + 2 decimals = 2 decimals
• 29.347 + 2.33 = 31.677  round to 2 decimals
• 29.347 + 2.33 = 31.68  2 decimals, 4 sig figs
Addition & Subtraction
• 2.45 x 105 + 3.1 x 104 = ?
• Must convert to the same exponent to see which is less precise
• Always convert the smaller exponent into the larger one
Addition & Subtraction
• 2.45 x 105 + 3.1 x 104 = ?
• 2.45 x 105 + 0.31 x 105 = ?
Addition & Subtraction
• 2.45 x 105 + 3.1 x 104 = ?
• 2.45 x 105 + 0.31 x 105 = ?
• 2.45 x 105 + 0.31 x 105 = 2.76 x 105
Practice
• Hebden p.28-34 #42-50, p.37 #55 (was HW)
• Add/subtract: Hebden p.40 #57
• All operations: Hebden p. 40 #58-59
• Hand in sig figs worksheet (online).