Full transcript
0:00Hello everyone , and today in this video
0:02, we will see how to write a result
0:04with its associated uncertainty . This
0:06will be valid for a series of
0:08measurements or a single measurement .
0:13So , let's start by taking an example .
0:15You measure a mass and you have its
0:17associated uncertainty , type A or type
0:19B , it doesn't matter , it will be the
0:20same . And now that you have both
0:23results , how do you write the final
0:25result ? Well , in high school , a single
0:28significant figure for the uncertainty
0:30will suffice . Why ? Well , given the
0:33quality of the experimenter and the
0:35equipment , that is enough . But that is
0:37not always the rule . So that means we
0:40will simply keep the 3 here . The other
0:43digits will be removed . So if we round
0:46up , that gives me a result for the
0:48standard uncertainty of 0.04 g . Now , if
0:53the uncertainty is 0.04 g , that means
0:56it will no longer make sense to go
0:59beyond this second decimal place . So ,
1:03we will remove the digits that are
1:05after the 5 here , which is the second
1:07decimal of our measurement , meaning the
1:107 and the 8 . So the last significant
1:13digit of the measurement must be at the
1:16same decimal position as the digit of
1:18the uncertainty . So that gives us a
1:21final result of 3.45 g . We can now make
1:26a correct sentence that indicates the
1:28result and its standard uncertainty .
1:30Here is the sentence : the measured
1:33value is m = 3.45 g with a standard
1:36uncertainty u ( m ) = 0.04 g . We have
1:40just seen that the measurement result
1:42is written with a number of significant
1:44figures in agreement with the
1:45uncertainty . It is the uncertainty that
1:48guides the number of significant
1:49figures of the measurement . And this is
1:51important when making a large number of
1:53measurements . Let's take an example .
1:55Let's take a stopwatch that measures to
1:57the tenth of a second . Let's perform
1:59duration measurements and calculate .
2:02You can go see the associated standard
2:04uncertainty in a previous video , and
2:06here the standard uncertainty is 0.05
2:09seconds . So we see that we will give
2:12our average at 10.92 seconds . We see ,
2:15therefore , that the precision of our
2:18average duration is greater than the
2:20precision of the equipment , here the
2:22stopwatch , which is measured to the
2:24tenth . So now , it's your turn to work
2:29and try to give me the results for each
2:32line of the uncertainty and the
2:35measured value here . So , if you have
2:41done it , you can pause , look , and
2:43compare your results . So , what should
2:46you remember from this video ? and note
2:49that the uncertainty is rounded up to
2:51keep only one significant figure and
2:53that the last significant figure of the
2:56measurement must be at the same decimal
2:58position as the figure of the
2:59uncertainty . That's all for this video
3:02and I'll see you soon for the next ones
3:04.