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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?.

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Tools for chemists

Tools for Chemists

Measurements and Numbers


The king s foot
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
Number of Pennies in a Jar

  • Exact or Inexact?


Height of pennies in a stack
Height of Pennies in a Stack

  • Exact or Inexact?



The great penny count1
The Great Penny Count

Machine Count = 116.

Which team is accurate? Precise?


The great penny count2
The Great Penny Count

Are errors random? Systematic?



Uncertainty
Uncertainty

  • What creates it?

  • How do we indicate it?


The recording uncertainty rule
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

Try It!


Significant figures

Significant Figures

The Horse and the Ribbon

0.19 lbs

1270 lbs


1270 lbs

+ 0.19 lbs

1270.19 lbs


Communicating significance
Communicating Significance

  • Significant Numbers and Place holders

    • Non-zero digits

  • Zeros

    • Leading: 0.0256

    • Confined: 20056

    • Trailing: 347000 or 347000.


Practice
Practice

  • 72.0

  • 51.700

  • 0.03400

  • 3.060

  • 450

  • 360,000


Vocabulary summary
Vocabulary Summary

  • Exact Number

  • Inexact number

  • Precision

  • Accuracy

  • Random error

  • Systematic error

  • Uncertainty

  • Significant figures


Sig figs and mathematical operations
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
Rounding Practice

  • Round to 3 sig figs

    • 72.311

    • 72.382

    • 72.353

    • 64.453

    • 72311

    • 72382

    • 72356


Multiplying and dividing with sig figs
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
    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
    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
    Assignment

    • Read 2.1-2.6

    • Do Problems in range 2.1 – 2.77


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