Measurements and Numbers 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 100 105 114 107 108 118 125 115 132 104 117 Avg = 116 + 16 Avg = 106 + 2 Avg = 116 + 2

Which team is accurate? Precise? The Great Penny Count Tom’s Team Sue’s Team Max’s Team 100 105 114 107 108 118 125 115 132 104 117 Avg = 116 + 16 Avg = 106 + 2 Avg = 116 + 2 Machine Count = 116. Which team is accurate? Precise?

Are errors random? Systematic? The Great Penny Count Tom’s Team Sue’s Team Max’s Team 100 105 114 107 108 118 125 115 132 104 117 Avg = 116 + 16 Avg = 106 + 2 Avg = 116 + 2 Are errors random? Systematic?

Does Your Measuring Tool Matter? Try it! Put a line approx. .5 m long on board. Get first student to measure w meter stick with only dm marked, second to use stick with cm, third stick with mm.

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

The Horse and the Ribbon Significant Figures The Horse and the Ribbon 0.19 lbs 1270 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. Do examples

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. 350.00 x 0.00072 3554/2.22 237 + 37 + 7 4.111 - 3.07 1.20 x (3.45 + 4.5) 0.500 x0.1723 x (0.6772 + 0.31)

Assignment Read 2.1-2.6 Do Problems in range 2.1 – 2.77