Calculations Using Sig Figs. Rounding Some of us are used to always rounding 5s up E.g. 20.5 21 In...

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).