Tools for Chemists

Measurements and Numbers

The King’s Foot

The story of a King, a Queen, and a carpenter who almost lost his life for the lack of a system of standard measurements.

Number of Pennies in a Jar

Exact or Inexact?

Height of Pennies in a Stack

Exact or Inexact?

The Great Penny Count

Tom’s Team Sue’s Team Max’s Team

100 105 114

107 108 118

125 107 115

132 104 117

Avg = 116 + 16 Avg = 106 + 2 Avg = 116 + 2

The Great Penny Count

Tom’s Team Sue’s Team Max’s Team

100 105 114

107 108 118

125 107 115

132 104 117

Avg = 116 + 16 Avg = 106 + 2 Avg = 116 + 2

Machine Count = 116.Which team is accurate? Precise?

The Great Penny Count

Tom’s Team Sue’s Team Max’s Team

100 105 114

107 108 118

125 107 115

132 104 117

Avg = 116 + 16 Avg = 106 + 2 Avg = 116 + 2

Are errors random? Systematic?

Does Your Measuring Tool Matter?

Try it!

Uncertainty

What creates it? How do we indicate it?

The “Recording Uncertainty” Rule

Record all digits which you can read with certainty off the measuring device, plus one estimated digit. The resulting numbers will all be significant.

Try It!

Student Balance

22 23

Research Balance 22.5

Significant Figures

The Horse and the Ribbon

1270 lbs0.19 lbs

How much do they weigh together?

1270 lbs

+ 0.19 lbs

1270.19 lbs

Communicating Significance

Significant Numbers and Place holders Non-zero digits

Zeros Leading: 0.0256 Confined: 20056 Trailing: 347000 or 347000.

Practice

72.0 51.700 0.03400 3.060 450 360,000

Vocabulary Summary

Exact Number Inexact number Precision Accuracy Random error Systematic error Uncertainty Significant figures

Sig Figs and Mathematical Operations

Rounding < 5: drop > 5 round up = 5: Round up if odd, drop if even If rounding to left of decimal, replace dropped

digits with placeholder zeros.

Rounding Practice

Round to 3 sig figs 72.311 72.382 72.353 64.453 72311 72382 72356

Multiplying and Dividing with Sig Figs

The number of sig figs in the answer (product or quotient) equals the number of sig figs in the multiplier or divisor with the fewest sig figs.

Huh? Area: 62.059 in x 72.6 in = 4505.4834 in2

Addition and Subtraction

The precision of the number resulting from an addition or subtraction operation is the same as that of the least precise number used to carry out the operation.

Huh? Huh?

Small Group Practice

Carry out the following operations and write the answer with correct sig figs, rounding properly.

1. 350.00 x 0.000722. 3554/2.223. 237 + 37 + 74. 4.111 - 3.075. 1.20 x (3.45 + 4.5)6. 0.500 x0.1723 x (0.6772 + 0.31)

Assignment

Read 2.1-2.6 Do Problems in range 2.1 – 2.77