Learning Targets
1.02B  I understand all measurements have uncertainty. I can estimate the magnitude of this uncertainty and evaluate experimental design to reduce uncertainty.
1.03B  I can use the range and average of a set of data to express a value and estimate its uncertainty. I can report these numbers with the correct number of significant figures.
1.04A  I can convert between standard metric units of measurement, and between English and metric units.
1.04B  I can convert between units when there is a unit in the denominator.
1.07C  I can take a set of data and represent on a graph with the correct model. I can follow the conventions for creating a graph and include error bars.
1.03B  I can use the range and average of a set of data to express a value and estimate its uncertainty. I can report these numbers with the correct number of significant figures.
1.04A  I can convert between standard metric units of measurement, and between English and metric units.
1.04B  I can convert between units when there is a unit in the denominator.
1.07C  I can take a set of data and represent on a graph with the correct model. I can follow the conventions for creating a graph and include error bars.
Can you...
 Select appropriate measuring devices
 Consider accuracy of measuring device and significant figures
 Collect data for the widest reasonable range of independent variable values.
 Use metric units, conversions and prefixes
Uncertainty
All measurements are estimates. The purpose of each measurement is to give us an idea about the physical properties of an object. Take a look at the cup of water below:
So really each measurement, is a range of values. The uncertainty is a way for us to express our measurement as a single best guess, but include all the reasonable values. We typically use +/ notation to say that the true value for our measurement could be anywhere from less than our best guess or more than our best guess.
For the beaker, we said the volume could be somewhere between 25 and 29. So my best guess would be 27 mL, but it could be 2 mL more or 2 mL less. I would then express that as 27 +/ 2 mL. This "2 mL" is our uncertainty.
In the graduated cylinder, we have a more precise measuring tool so we can decrease our uncertainty. If we know the volume is between 27 mL and 28 mL, my best guess would probably be 27.5 mL but it could be 0.5 mL or 0.5 mL less. I would then express that as 27.5 +/ 0.5 mL. This "0.5 mL" is our uncertainty.
For the beaker, we said the volume could be somewhere between 25 and 29. So my best guess would be 27 mL, but it could be 2 mL more or 2 mL less. I would then express that as 27 +/ 2 mL. This "2 mL" is our uncertainty.
In the graduated cylinder, we have a more precise measuring tool so we can decrease our uncertainty. If we know the volume is between 27 mL and 28 mL, my best guess would probably be 27.5 mL but it could be 0.5 mL or 0.5 mL less. I would then express that as 27.5 +/ 0.5 mL. This "0.5 mL" is our uncertainty.
Sources of Uncertainty
When we have a source of uncertainty that comes from a random and unpredictable action, we can use an average for determining a best guess.
Imagine you are timing how long it takes someone to run the hundred meter dash. You have to make a judgement when they start running, react and start timing, then judge when they reach the finish line, react and stop timing. All of this reaction time will not likely be the same for each repeated trial. So when you have this random error/uncertainty you can get the best estimate by using an average.
Random error from multiple measurements:
Imagine you are timing how long it takes someone to run the hundred meter dash. You have to make a judgement when they start running, react and start timing, then judge when they reach the finish line, react and stop timing. All of this reaction time will not likely be the same for each repeated trial. So when you have this random error/uncertainty you can get the best estimate by using an average.
Random error from multiple measurements:
 Only way to estimate is with multiple measurements that SHOULD BE THE SAME
 Uncertainty = Range/2, rounded to 1 sig fig
 Best Guess = Average, rounded to same decimal place as uncertainty
Unit ConversionsHow to convert units:

