Day 8, Friday, 4 September, 2015 Uncertainty and Significant Figures

Unit Analysis Lecture

Uncertainty Significant Figures

Dimensional AnalysisUnit Analysis

you wish

Given units = Unknown units

Given (1) _ Unknown = Unknown (Given) (1)

actually does

Day 8, Friday, 4 September, 2015

New Stuff

Good things to know 2.54 cm/in 2.2 lbs/kg 39.5 in/m 1,000 kg/ton (2,200 lbs/ton) Water’s density is 1 ton/m3 or 1 g/cc

Uncertainty

Instruments always have flaws

Measurements always involve estimation

Take measurements from the perpendicular

Meter stick demo

The last digit is estimated

The certain digits and the estimated digit of a measurement together are significant digits.

Reliability

Precision Repeatability of a measurement

Accuracy Agreement with an accepted value

Lucky Duck

High AccuracyLow Precision

Lucky Duck 2

Low AccuracyHigh Precision

Unlucky Duck

High AccuracyHigh Precision

When is Zero significant? As a measured value zero is significant

A zero between two other non zero numbers is always significant

As a placeholder zero is not significant Leading zeros before decimal point are meaningless Leading zeros are not significant Unmeasured trailing zeros are not

significant

The two uses of zero

1. As an actual value The number between 1 and -1

significant

2. As a placeholder The value of a column

Not significant

0.0023405670000

0.0023405670000 not significant0.0023405670000 significant*0.0023405670000 significant0.0023405670000 totally useless* If measured (They bothered to write

it so it is assumed to be significant)

Multiplying and dividing Sig Figs

A chain is only as strong as its weakest link.

If I give $137.58 to 972 people then I have given away $133,727.76.

If I give away $137.58 to about 1,000 people have I given away $133,727.76? NO, I have given away about $140,000.

If I give away about $140 to 972 people have I given away $133,727.76?NO, I have given away about $140,000.

A nice paint job on a sloppily built car looks sloppyA sloppy paint job on a nicely built car looks sloppy

Use the least number of Sig Figs given (regardless of where the decimal point is).

1.23456789 x 1.2 = 1.51.23456789 x 1.20000000 = 1.48148147

1.23456789 / 1.2 = 1.01.23456789 / 1.20000000 = 1.028806575

Multiplying or Dividing

Adding and Subtracting Sig Figs

Use the smallest decimal column that is common to both numbers (counted from the decimal point).

1.23456789 + 1.2 = 2.41.23456789 + 1.23456789 = 2.46913578

1.23456789 - 1.2 = 0.01.23456789 - 1.20000000 =0.03456789

Format for Homework Problems

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