Chemistry Lesson: Introduction to Measurements
Summary
TLDRDr. Kent's video on getchemistryhealth.com offers a concise guide to scientific measurements, emphasizing the importance of recording both numbers and units. It distinguishes between exact numbers, which are defined or counted without ambiguity, and inexact numbers, which involve approximation. The video delves into the concepts of accuracy and precision in measurements, illustrating them with examples. It also explains the significance of significant figures in indicating measurement precision and error, providing practical examples of how to determine significant figures when measuring length, volume, and temperature.
Takeaways
- 🔍 In scientific measurements, both the number and its unit are essential for accurate data recording.
- 📏 Exact numbers in science are either defined as true or obtained through counting without ambiguity.
- 📐 Measurements in science are inexact due to the inherent approximation and estimation involved in determining values.
- 🎯 The accuracy of a measurement refers to how close it is to the accepted or true value.
- 🔄 Precision in measurements indicates the consistency or closeness of a series of measurements to each other.
- 📊 To evaluate data, consider both accuracy (closeness to the true value) and precision (consistency of measurements).
- 📈 Significant figures represent the precision of a measurement and are indicated by the number of digits recorded.
- ✏️ When recording measurements, include all known digits and estimate one additional digit beyond the clearly marked ones.
- 📏 The number of significant figures is directly related to the precision of the measurement; more digits indicate less error.
- 🌡️ Examples in the script illustrate how to determine significant figures when measuring length, volume, and temperature using various tools.
Q & A
What is the importance of including units when recording scientific measurements?
-Including units in scientific measurements is crucial as it provides context and meaning to the numerical data, allowing for accurate interpretation and comparison of results.
What is the difference between exact and inexact numbers in the context of scientific measurements?
-Exact numbers are defined to be true or obtained through counting without ambiguity, while inexact numbers are obtained through measurements that involve some degree of approximation or estimation.
Why is it necessary to estimate only one additional digit beyond the clearly marked values on measuring instruments?
-Estimating only one additional digit ensures the recorded measurement reflects the precision of the instrument and avoids overestimating its accuracy.
How does the accuracy of a measurement relate to its true value?
-The accuracy of a measurement is determined by how close it is to the accepted or true value, indicating the correctness of the measurement.
What does precision in measurements signify and how is it evaluated?
-Precision signifies the consistency of a set of measurements, indicating how closely related a series of measurements are to one another. It is evaluated by observing the closeness of multiple measurements.
What is the significance of significant figures in scientific measurements?
-Significant figures indicate the precision and reliability of a measurement, with more significant figures suggesting a more precise and less erroneous measurement.
Can you provide an example of how to determine the significant figures when measuring the length of an object with a ruler marked in centimeters?
-When measuring with a ruler marked in centimeters, you record all clearly marked digits and estimate one additional digit. For example, if the object is between 4 and 5 centimeters, you might record it as 4.2 cm, indicating two significant figures.
How does the precision of a measuring instrument affect the number of significant figures you can record?
-The precision of a measuring instrument directly affects the number of significant figures that can be recorded. More precise instruments allow for more significant figures, indicating a higher level of precision and less error.
What is the difference between accuracy and precision in the context of the data sets shown in the video?
-In the video, data set D is both accurate and precise, being close to the target value and consistent. Data set B is accurate but imprecise, being close to the target but not consistent. Data set C is precise but not accurate, being consistent but off-target. Data set A is neither accurate nor precise, being both off-target and inconsistent.
Why is it incorrect to record a measurement as 22 on a thermometer marked with tens and ones places?
-Recording a measurement as 22 on a thermometer marked with tens and ones places is incorrect because it implies that the ones place is estimated, which is not the case. The correct approach is to estimate one more digit beyond the clearly marked ones place, such as 22.1 or 22.2.
Outlines
🔍 Introduction to Scientific Measurements
Dr. Kent introduces the concept of scientific measurements, emphasizing the importance of recording both the numerical value and its unit. He distinguishes between exact numbers, which are defined or counted without ambiguity, and inexact numbers, which are measured and involve estimation. The video explains the difference between accuracy, which is how close a measurement is to the true value, and precision, which is the consistency of repeated measurements. Examples are used to illustrate the concepts of accuracy and precision, with visual aids to help viewers understand the difference between measurements that are accurate but imprecise, inaccurate but precise, and neither.
📏 Understanding Accuracy and Precision with Data
This section delves deeper into the application of accuracy and precision with real-world data examples. Dr. Kent presents four sets of data and guides viewers to determine which set is both accurate and precise by comparing the data to a known true value. The discussion continues with examples of data that are accurate but imprecise, and data that are neither accurate nor precise. The concept of error in measurements is introduced, linking it to the number of significant figures, which indicate the precision and error margin of a measurement.
🔢 Significance of Significant Figures in Measurements
Dr. Kent explains the concept of significant figures, which are the known digits in a measurement plus one estimated digit. He clarifies that significant figures apply only to measurements, not to exact numbers. The video demonstrates how to determine significant figures when measuring the length of an object with a ruler, emphasizing that one should estimate only one additional digit beyond the clearly marked ones on the measuring device. Examples are provided to show how different measuring tools with varying levels of precision can affect the number of significant figures and the precision of the measurement.
🌡️ Estimating Measurements and Significant Figures
In this segment, Dr. Kent demonstrates how to estimate measurements and determine significant figures when using different measuring tools like rulers, graduated cylinders, and thermometers. He shows how the precision of the tool affects the number of significant figures one can record. The video includes a practical exercise where viewers are invited to estimate temperatures on thermometers and then compares their estimates with the correct method of recording temperatures with the appropriate number of significant figures.
Mindmap
Keywords
💡Measurement
💡Unit
💡Exact Numbers
💡Inexact Numbers
💡Accuracy
💡Precision
💡Error
💡Significant Figures
💡Estimation
💡Graduated Cylinder
Highlights
Introduction to scientific measurements and the importance of recording data with units.
Explanation of the difference between exact numbers and inexact measurements in science.
Definition of exact numbers as those defined to be true or obtained through counting.
Example of exact numbers: one dozen equals 12, one week equals seven days.
Inexact numbers result from measurements that involve approximation and estimation.
Measurements like temperature and weight are inexact due to the inherent estimation.
Criteria for evaluating measurements: accuracy and precision.
Accuracy refers to how close a measurement is to the accepted value.
Precision indicates the consistency of a series of measurements.
Illustrative examples using targets to demonstrate accuracy and precision.
Explanation of significant figures and their role in indicating measurement error.
Recording measurements with the correct number of significant figures for precision.
How to estimate one digit beyond the clearly marked values on measuring devices.
Example of measuring length with a ruler and estimating to the nearest tenth or hundredth.
Different levels of precision demonstrated with various measuring tools like rulers and burets.
Practical examples of measuring liquid volume in beakers and graduated cylinders.
Guidance on reading temperatures on thermometers with different levels of precision.
Final thoughts on the importance of significant figures in scientific measurements.
Transcripts
well hello and welcome to
getchemistryhealth.com
my name is dr kent and in this video i'm
going to give you a quick introduction
into how to make scientific measurements
so of course in science we perform
different types of experiments and when
you perform experiments well you collect
data
and that data is then recorded somewhere
so for example maybe you go in a lab you
do an experiment and you write down 52.8
as your data or your measurement well
what's wrong with this measurement
well 52.8 watt right we need some kind
of a unit so if you were to say 52.8
kilometers or 52.8 degrees fahrenheit or
hours or minutes that would make a lot
more sense so whenever you record a
measurement in science you always have
to record both the number and a unit
now there are actually two different
types of numbers that we work with in
science the first type are known as
exact numbers and exact numbers are
those that have been defined to be true
or those that you can obtain through
counting so there's no kind of ambiguity
there's no guessing there's no
estimating there's no approximating for
example one dozen has been defined to be
exactly 12 it's not around 12 it is
exactly 12 again it's been defined to be
true
one week is exactly seven days
one dollar is exactly a hundred pennies
one kilometer is exactly a thousand
meters again these are all things that
have been defined and i'm sure you can
think of lots of others like for example
one hour is exactly 60 minutes one
minute is 60 seconds one foot is exactly
12 inches again these have all been
defined so they're exact there's no
estimating there's no approximating
now exact numbers can also be numbers
that you obtain through counting so you
physically count one two three four five
six seven so we know there are exactly
seven quarters
so we're not guessing we're actually
defining how many quarters there are
by contrast measurements are always
inexact again when you're measuring
something it's not been defined you're
trying to determine what the value is
and again the reason it's inexact is
there's some kind of approximating
there's some kind of estimating
so for example maybe you measure the
temperature of something and it's 82.4
degrees fahrenheit or you measure your
weight on the bathroom scale and it
comes up 178 pounds
or you measure the length of a race and
it's 100.0 meters these have all been
measured so these are called in exact
numbers we're not saying that person is
exactly 178 pounds but they're
approximately 178 pounds
now when it comes to evaluating
measurements we can evaluate them
according to two different criteria the
first one is known as the accuracy of
the measurement and that's how close the
measurement is to the target to the
accepted value
and the other one is the precision of
that measurement and that's how close a
series of measurements are to one
another
so for example if you're taking three or
four or five measurements how close are
all those measurements to one another
so another way to think about this is
accurate or accuracy is how correct your
answer is how close to the true value is
it
and precision or being precise is how
consistent you are
so let me give you a couple examples
just to help illustrate this
so let's look at these four different
targets a b c and d and we want to
determine
um which set of data or which set of
these little blue shots or circles
are accurate
and precise which ones are accurate but
they're not precise etcetera so again
accurate means you are close to the
bullseye you are right where you want to
be that's the correct answer
and precise means how close together how
consistent is your data or your shots in
this case
so which of these are both accurate
they're on target and they're precise
they're very consistent they're very
close together
well of course it looks like d because
you see they're on target and they're
all close together so they're accurate
and they're also precise they're also
consistent so which of these is accurate
but they're not consistent they're
imprecise
well that looks like b because you can
see they are all then pretty close onto
the target but they're more spread out
they're not all clustered as close
together as they were up on d
now three which of these targets shows
some data that is not accurate but it is
precise so in other words it's very
consistent but it's consistently wrong
well that looks like c because you can
see the data it's all clustered and very
close together very consistent very
precise but it's off target
so it's not accurate
and how about neither accurate nor
precise or inaccurate and imprecise of
course that must be a because they're
all spread out and they're not on the
target
now let's try this with some actual data
like you might see in the lab so here
are four different sets of data a b c
and d and it tells us that the true
value is 55.4 kilograms so first we want
to figure out which set of data is both
accurate so it's close to our true value
55.4
and it's precise all the measurements
are very close to one another so what do
you think a b c or d
well it looks like a because you can see
the values are all very close to one
another which means they're precise
and when you average them out the
average is very close or actually
exactly on the true value
so which of these are accurate but
they're not as consistent they're
imprecise
well it looks like c because when you
average these out yes you get a value an
average here that's very close to the
true value but the data is much more
spread out you see here they're all
they're all clustered close together
0.3.4.5
here it's ranges from 54.7 all the way
up to 55.9
how about number three they're not
accurate but they are precise or they
are consistent
well that looks like b
because the average of these three
values 54.9
is not on target right it's not real
close to the actual value but they are
very close to one another they're only
off by 0.1 more here 0.2 more here etc
so they're very close
and then the last one
d
it's not accurate because the average of
the three values is off target from the
known value
and they're all spread out too so that's
inaccurate
and imprecise
so whenever you make measurements in
science there's always going to be some
degree of error associated with it you
can't make a perfect measurement with no
error
so the more precise the measurement is
well the less error is contained in it
now error in a measurement is indicated
by the number of what are called
significant figures or significant
digits so if a number has more
significant digits that means it's more
precise and has less error
so let's talk about significant figures
how do we record those so when you're
making a measurement you want to record
all of the known digits all the ones
that are clearly marked on the device on
the thermometer on the ruler on the
graduated cylinder
plus
one final estimated digit so you only
estimate one more digit beyond whatever
is clearly marked
this indicates the precision of a
measurement
now remember sig figs only apply to
measurements right not to exact numbers
again if something has been defined to
be true like one foot equals 12 inches
that is exactly 12 it is infinitely
precise in other words there is no error
in that whatsoever
so let's just look at an example
so here's a ruler and it's marked in
centimeters we can see
and we want to measure the length of
this rod
so what we do is we record whatever
numbers are clearly marked on the ruler
and then we're going to estimate
one more digit beyond that so i can see
it's clearly marked it's four point
something
and then i'm going to estimate one more
so you might say
4.2 centimeters
or maybe you think well i think it's
closer to three so maybe you say 4.3
centimeters
but what you don't do is you estimate
more places than just one and say i
think it's
4.217 you can only estimate one more
digit beyond whatever is clearly marked
on the device
so this ruler is marked in ones so we
can estimate out to tenths so 4.2 and
that tells you then you're within plus
or minus 0.1 so it might be 4.1
centimeter it might be 4.3 centimeter
and those are all fine if you were to
write down 4.3 i would write down 4.2
someone else would write down 4.1 those
are all within the same realm of
precision because they're all within 0.1
of the correct answer because again that
last digit is the one you're estimating
how would you make that measurement on
this ruler so this ruler is more precise
because it allows us to have
more significant digits because this one
is marked in one so four
five six it's also marked in tens so
here's 4.1 4.2 4.3
so now we can say okay i know it's 4 for
sure
and i know it's between 0.2 and 0.3 so
0.2 something for sure
but again i always have to estimate one
more so maybe i think it's right in the
middle so i'm going to say
4.25 centimeters
so up here we had
4.2 centimeters here we have 4.25
so you can see this one had two digits
this one has three digits or three
significant figures so more digits
indicate that this value is more precise
because this one we were estimating the
hundredths place
in this one on ruler a we were only
estimating out to the tenths place
so this ruler again gives us a more
precise measurement and has less error
in it because it produces values with
more significant digits
let's try that again on this paper clip
how would you record the length of this
paper clip on this ruler
so again we see it's clearly marked in
ones
so i know it's between two and three so
it's
two point something but i have to
estimate one more place again i can't
estimate more or less than one so
two point
let's say three centimeters or maybe you
say
2.4 centimeters
again both of those answers are fine
because we're both estimating in the
tenths place
now if you were to have a different
place here and you were to say three
point something that would be totally
wrong because it's clearly two something
now how about on this ruler well this
one is marked in ones and tenths so
again we can be more precise
so now you might say well two for sure
and then we see it's pretty clearly
right on the three here
so 2.3
but we can't stop there we have to go
one more again if i were just to write
this down as 2.3 that would say the ones
are what i knew for sure
but i'm estimating the tenths and that's
not true because the tenths are marked
so i have to estimate the hundredths
so if you think it's right on
the 3 you would say
2.30 or maybe you think it's slightly
below so you might say
2.29 centimeters
again those are both fine because we're
both just off here in the hundredths
place which is where that estimated
digit is
okay let's try a few more examples just
to drive this point home how would you
record the volume of the liquid in this
beaker well again you want to record
whatever place is clearly marked and
estimate one more digit after that so
here we see it's 20 something
we're going to estimate one more
looks like it's maybe 28 so 28
milliliters
again if you say 27 or 29 that's fine
because we all agree on the tens place
it's the ones place that we're
estimating
now over here on this graduated cylinder
you see now it's marked in ones
so we know the ones for sure
28 something
but again we have to estimate one more
place so that would be tenths place
so you might say
28.2
milliliters or maybe you think it's 28.3
milliliters again both are fine
because we're estimating
in the tenths place now
now over here on the buret this is even
more precise we're going to have more
significant digits because now the ones
are marked 28 29 30
and the tens are marked so 28.1 0.2 0.3
but again i still have to go one more
so i know for sure it's 28.3 i'm going
to estimate one more and say
maybe two so 28.32 again if you think
it's 28.31 that's fine
because we're estimating out here in the
same digit
now notice how these values all got more
precise so this one had two significant
digits so it's the least precise
then we went out to tenths place so that
gave us three significant digits that's
more precise and then four significant
digits so that's more precise
okay one last example let's go ahead and
take a minute to practice reading the
temperatures on these three thermometers
so go ahead pause the video and just
take a quick second and write down your
three best guesses and then when you're
ready to have your answers checked go
ahead and hit play
okay so what do we know for sure was
marked in tens here's 20 here's 30 it's
also marked in ones so 21 22 23
so i know for sure it's 21 point
something but i have to go one more
digit
so maybe i think it's
21.2 and we'll assume this is degrees
celsius since it doesn't tell us
but if you said 21.3
again that's fine as long as we're
estimating out in the tens
21
that would be completely wrong right
because 21 would say
tens are what i know for sure and i'm
estimating the ones and that's not true
i know the tens and the ones so i have
to estimate tenths place
how about over here on this thermometer
well again tens are marked and ones are
marked so i know it's 22
but again i can't just write 22 i have
to estimate one more so if it's right on
22 then i have to put point zero
one more time why would 22 be wrong
because that would say you were
estimating the ones place which is not
the case
we are estimating the tenths place
because the ones are marked
okay how about this last thermometer how
would you do that
well it's a little hard to see but we
can tell tens are marked so i know it's
20 something
ones are marked 21 22
and even the tenths so it's just above
0.1
but again i can't stop there i have to
go a little farther so i'm going to say
22.12 degrees celsius
you might say
22.11 degrees celsius or 22.13
degrees celsius
but again we're all estimating out here
in the hundredths place because we all
agree that the tens the ones in the
tenths are all clearly marked and the
estimating has to occur in the
hundredths place
so which of these values is the most
precise again the one that has more
significant digits is more precise
well i hope you enjoyed this quick video
on how to take scientific measurements
using the correct number of significant
digits for even more videos on
significant digits including how to use
them in calculations please come visit
me at getchemistryhelp.com
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