Significant Figures and Measurement
Summary
TLDRThis video script offers a comprehensive guide on significant figures in measurement, emphasizing accuracy and precision. It explains the concept of significant figures as all known digits plus one estimated digit. The script demonstrates how to use various lab equipment, including triple beam balances, centigram balances, graduated cylinders, and rulers, to accurately measure mass and volume. Each device's calibration and reading process is detailed, highlighting the importance of estimating to the appropriate decimal place based on the device's precision.
Takeaways
- 🔍 Significant figures are crucial in scientific measurements, representing all digits known with certainty plus one estimated digit.
- 📏 Accuracy in measurement refers to how close the measurement is to the true value, while precision is about the repeatability of the measurements.
- 🧭 To determine significant figures, one must read all certain digits and estimate the final digit, with different devices estimating to different decimal places.
- 🔬 Calibration of measuring devices is essential before taking measurements to ensure accuracy.
- ⚖️ When using a triple beam balance, start with the largest rider and work down, adjusting for precision with the smallest rider.
- 📊 Centigram balances or hanging pan balances offer higher precision in mass measurements, estimating to the thousandth of a gram.
- 💧 For substances that cannot be directly weighed, such as liquids or powders, use a container and subtract its mass from the total to find the substance's mass.
- 🧪 Graduated cylinders are preferred for volume measurements due to their precision, with markings for every milliliter or tenth of a milliliter.
- 🌡️ When reading a graduated cylinder, always read at eye level and take the measurement at the bottom of the meniscus for accuracy.
- 📏 Meter sticks or rulers are used for length measurements, with precision to the millimeter or tenth of a centimeter, depending on the markings.
Q & A
What is the difference between accuracy and precision in measurements?
-Accuracy is how close a measurement is to the correct or true value, while precision refers to the repeatability or consistency of the measurements.
What are significant figures and how are they used in measurements?
-Significant figures are all the digits that are known for certain plus one estimated digit. They are used to indicate the precision of a measuring device and to determine the number of reliable digits in a measurement.
How do you determine if a digit is certain or uncertain when measuring?
-A digit is certain if all 10 graduations or marks are indicated on the measuring device. For example, for the ones place to be certain, all digits from 1 through 9 must be marked between the tens place.
What is the procedure to calibrate a triple beam balance?
-To calibrate a triple beam balance, ensure all riders are set to zero, adjust the calibration knob under the pan until the balance lines up, and make finer adjustments as needed until the balance is level.
How do you measure the mass of an object using a triple beam balance?
-Place the object in the center of the tray, start with the hundred gram rider, and adjust the riders until the balance is level. Record the mass using significant figures.
What is the difference between a centigram balance and a triple beam balance?
-A centigram balance, also known as a hanging pan balance, increases precision by introducing another rider at the tenth of a gram position, allowing for more precise mass measurements.
How do you read a measurement from a graduated cylinder?
-When reading a graduated cylinder, ensure it's level and at eye level, and read the bottom of the meniscus, which is the curved surface of the liquid being measured.
Why is it important to consider the last digit as an estimate when measuring?
-The last digit in a measurement is an estimate, which allows for some leeway. This is because the exact position between graduations can be subjective, so accepting a range (e.g., from 0.61 to about 0.64) is more practical.
What is the significance of the marks on a measuring device in relation to significant figures?
-The marks on a measuring device indicate the level of precision. Each marked graduation represents a certain place value, and the last marked place is known for certain, with the next place being the estimated significant figure.
How do you measure the volume of a liquid that cannot be directly placed on a weighing pan?
-For liquids or powders that cannot be directly placed on a weighing pan, you can measure the mass of the container first, then add the sample, measure the total mass, and subtract the mass of the container to find the mass of the sample.
Why are graduated cylinders preferred over beakers for measuring volume?
-Graduated cylinders are preferred over beakers for measuring volume because they have finer markings, typically every milliliter, allowing for more precise volume measurements.
Outlines
🔍 Understanding Significant Figures in Measurement
This paragraph introduces the concept of significant figures in the context of measurement accuracy and precision. It explains that accuracy refers to how close a measurement is to the true value, while precision refers to the consistency of repeated measurements. Significant figures are defined as all digits known with certainty plus one estimated digit. The paragraph emphasizes the importance of understanding significant figures when using any measurement device, as it dictates the level of precision required for reporting values. It also discusses how to determine certain and uncertain digits on a measuring device, with examples including balances that estimate to different decimal places of a gram.
🧪 Practical Application of Significant Figures in Lab Equipment
This section delves into the practical application of significant figures using lab equipment such as triple beam balances and hanging pan balances. It demonstrates how to calibrate these balances for accuracy and how to read measurements, including the estimation of the last significant figure. The paragraph explains the process of measuring mass with these balances, highlighting the importance of identifying certain and uncertain digits. It also touches on the use of containers for measuring the mass of substances that cannot be directly placed on the balance, such as liquids or powders.
📏 Measuring Volume with Precision Using Graduated Cylinders
The paragraph focuses on the use of graduated cylinders for measuring volume with precision. It explains that the level of precision depends on the markings on the cylinder, with some cylinders marked for every milliliter. The video script demonstrates how to read a graduated cylinder accurately, including tips for pouring liquids, removing air bubbles, and reading the meniscus correctly. It also discusses the importance of using the correct technique to ensure the accuracy of volume measurements.
📏 Measuring Length with a Meter Stick or Ruler
The final paragraph discusses the use of a meter stick or ruler for measuring length. It highlights the importance of aligning the end of the ruler with the object being measured and the precision offered by the ruler's markings, which are typically in centimeters and millimeters. The paragraph demonstrates how to read the ruler accurately, focusing on the estimation of the last significant figure, and provides an example of measuring the length of an index card.
Mindmap
Keywords
💡Significant Figures
💡Accuracy
💡Precision
💡Measurement
💡Triple Beam Balance
💡Calibration
💡Graduated Cylinder
💡Meniscus
💡Estimation
💡Ruler
Highlights
Introduction to significant figures and their importance in measurement accuracy and precision.
Definition of significant figures as all digits known for certain plus one uncertain digit.
Explanation of how to read measurements using significant figures on different devices.
Procedure for calibrating a triple beam balance and ensuring accurate measurements.
Technique for measuring mass using a triple beam balance with an emphasis on significant figures.
Use of a centigram balance for increased precision in mass measurements.
Method for measuring the mass of a liquid using a container and subtracting the container's mass.
Discussion on the limitations of using beakers and erlenmeyer flasks for precise volume measurements.
Proper use of a graduated cylinder for accurate volume measurements, including reading the meniscus.
Technique for reading a narrow graduated cylinder with marks for every milliliter.
Measurement of length using a meter stick or ruler, focusing on significant figures.
Procedure for aligning a meter stick with an object for accurate length measurement.
Importance of reading the bottom of the meniscus in a graduated cylinder for precise volume measurement.
Guidance on making an estimate for the last significant figure in a measurement.
Advice on handling graduated cylinders to prevent spills and ensure accurate readings.
Transcripts
[Music]
today we're going to be covering
significant figures and how they relate
into measurement
now i want you to think back to the
measurement lab we had already done
we're going to think about what we did
and how we can improve it going forward
a key component of all measurements
involve accuracy and precision accuracy
is how close we are to the
correct number precision is how
repeatable our values are
anytime we're taking measurements we
have to use significant figures to
determine what place to report our
values to
the definition of significant figures is
very useful the definition itself can
actually describe to us how to use any
measurement device we could want the
definition of significant figures
is all digits that we know for certain
are known with certainty
plus one uncertain or estimated digit
in order to use that definition we read
all of the digits that we know or the
device tells us for certain
so all of the digits that it has passed
and finally we estimate for final digits
each measurement
must include an estimate different
devices have different
positions for their estimates for
example balances could estimate to the
hundredth of a gram to the tenth of a
gram
and in some cases to the thousandth of a
gram so we have to be able to identify
by looking at our device
exactly where we need to report our
measurements to a key component of this
is knowing if a digit is certain or not
a digit can only be certain if
all 10 graduations or marks are
indicated on the device for example for
the ones placed to be known for certain
all digits from 1 through nine have to
be marked in between the tens place
let's go to the lab and see what this
looks like with different devices
now that we've talked about what
significant figures are let's see how it
can relate into
measurements as well as precision and
accuracy
we're going to use the definition of
significant figures to be able to learn
how to read
each different device that we might be
using in a lab
or any device we might be using to take
a measurement in general the first
device we're going to look at is a
triple beam balance
first thing you need to do anytime
you're using a triple beam balance is
make sure all of the riders are set to
zero
at the far left after you've made sure
the riders are set to zero
you need to look at the far right where
your balance is
set and make sure that those lines line
up
in this case they don't which means the
balance still needs to be calibrated
in order to calibrate it you need to
look at the left under the
pan the calibration knob for the triple
beam balance is underneath
the pan you need to adjust it until the
balance lines up in this case
the balance is higher than zero
so i need to move the mass inward so i'm
going to turn the knob
so that the mass goes inward
[Music]
as i get close i'll make finer
adjustments i'm going to start by making
a large adjustment until i see that it's
very close
then once i get close i'll start making
finer adjustments
in this case i've overshot it a little
bit so i need to bring it back
out and we'll make a fine adjustment
let the balance steady and see where
level is
when you're checking to see if the
balance is calibrated you want to get
down to eye level to see to make sure
you're looking at the proper level
as you go now we're ready to measure the
mass of our object the object i've
chosen for this one
is a roll of tape you put the object in
the center of the tray
and always start with the hundred gram
rider
in this case i move it up to 100 that's
too much mass
i then move to the 10 gram rider
making sure to find the notches each
time
after it drops by i know i've gone too
far so it's not quite 60 but it's more
than 50.
finally i use the
one gram rider and i recommend using a
pen or a pencil to help this move
because it does stick to your fingers
[Music]
and at this point it rides freely so we
need
to make sure that as we're adjusting it
we are making
fine movements
at this point i'm going to continue
moving it until the
lines on the right line up
now that i can see the lines have lined
up perfectly i know that
this is balanced out and i can record
the mass
using the definition of significant
figures i can
measure the mass now i use all of the
digits i know for certain or i know for
certain that it is more than
in this case using the tens rider it is
more than 50.
using the ones rider it is more than six
so i know the mass is 56 and i can zoom
in
on the ones rider to be more precise
with my measurement after i zoom in on
the ones rider
i notice that each mark between the 6
and the seven
is one tenth of a gram because each
tenth of a gram
is marked i know that digit for certain
in this case i know it's 56.6
because the rider is pointing just to
the right
of 0.6 grams now i use the last part of
the definition
to make an estimate in this case
the mass of the roll of tape
is 56.62
grams i'll give some leeway as you're
making measurements because the last
digit is an estimate
you get a little bit of leeway i would
accept anything from 0.61
to about point six three or point six
four
another type of balance you might see
and we will periodically use this year
is either called a centigram balance or
hanging pan balance
it increases the precision of your mass
measurements
because it introduces another rider at
the tenth of a gram position
as you can see after i've zoomed in it's
marked
for every tenth of a gram and in between
every tenth of a gram we
see 10 marks so this one is precise
to the thousands place because every
hundredth
is marked for this type of balance the
calibration knob is up here on top
that is how you calibrate and make sure
that your balance is
accurate after i have my balance
calibrated
i put the object that i'm interested in
measuring the mass in the pan
and i follow the same procedures i start
with 100 gram
ryder 10 gram the 1 gram and then i move
to the 10th of a gram rider
[Music]
as you can see this balance is a little
more difficult to use it takes a little
more care
because of the added precision now that
it's balanced out
let's take a look at the reading to read
this
we read all the digits known with
certainty so everything that we know for
certain that it has passed
we know that it didn't pass 100 so our
first digit is the five
in the tenths place for 50. our ones
measurement is six so we know it's 56.
we then move to the tenth of a gram we
can see that it's very clearly past
0.7 so it's 56.7 something
i'm going to zoom in on that section and
take a closer look
after i've zoomed in into this section i
see that the arrow
is pointing just to the left of a mark
the mark the last mark that it has
passed is 0.77
so at this point i know it's 56.77
and i have to make my estimate because
the arrow is much closer to the mark on
the right
a good estimate for the thousands place
in this case would be
nine so the mass for this object is
56.779
grams something to consider when you're
measuring the mass of something
that can't be directly set on the
weighing pan
is to use another container to measure
it
for example if i had a sample of water
in a graduated cylinder that i wanted to
know the mass of
i would then need to find the mass of
the container that i'm going to put it
in first
i determine the mass using the riders
i would then pour the sample into
my container
i would then measure the mass of the
container
and the sample and subtract out the mass
of the container
to measure the mass of the water so
anytime we need
a sample that cannot be directly put on
such as a powder or a liquid
you'll have to use a container such as a
beaker or weighing boat and you'll have
to subtract out
the value of that beaker or weighing
boat
the next set of tools we're going to
look at are tools that measure
volume we're going to start with the
beaker
looking at the beaker the first thing we
should notice is that it is only marked
for every 100 milliliters
which tells us the only digit we know
for certain is the hundreds place
so our estimate will be to the 10
milliliters in this beaker
so generally we don't want to use a
beaker to measure volume we can use it
if all we have to do is estimate but a
beaker would not be the best way to
measure volume
next up we have an erlenmeyer flask we
can see that it's only measured
every 50 milliliters so it too is only
precise to the 10 milliliter
mark erlenmeyer flasks typically
aren't used to measure volume for that
reason as well
next up we have a graduated cylinder
graduated cylinders can vary and how
they're marked
i'm going to zoom in on the marks and
we're going to figure out what place
that the graduated cylinder is precise
to
when i zoom in you can see that there
are 10 marks between
60 and 70 milliliters that means
every one milliliter is marked on the
graduated cylinder
using our definition of significant
figures we know for certain
every one milliliter so our estimate in
this case will be to the tenths place
so let's take a look at how to read a
graduated cylinder
when i'm using a graduated cylinder i
want to make sure that the plastic
collar
is near the top it's an extra layer of
protection
to help prevent breaking this isn't used
to measure
it's just to help prevent breaking if it
were to get knocked over
when i'm ready to start measuring with a
graduated cylinder
i can pour either from a beaker or flask
i want to pour from some device into the
graduated cylinder
and i want to get close to the value
that i want to measure
in this example i want to measure 50
milliliters so i'm going to fill
the graduated cylinder up until it gets
close to 50 milliliters
and remember when you're pouring you
want to commit
at the beginning and the end to prevent
spilling
i need to get air bubbles out i can
gently tap it on the table
or gently tap the graduated cylinder to
get the air bubbles out
because they will affect my reading as
well
when i read it there's a couple
different options i can either
lean into it to read or
i can lift the graduated cylinder to
read it
you want to pick one of the two you do
not want to squat down if you squat down
you expose yourself to being
it's getting spills on your body
so you can either lean into it
or you can carefully lift the graduated
cylinder
if you hold it near the top you can make
sure that it stays level
and vertical that way once you've gotten
to eye level with your graduated
cylinder
you want to make sure that you are
reading the bottom of the meniscus
the meniscus is the curved surface of
the liquid that we are measuring
in water's case the meniscus curves down
so you'll see
two distinct layers where the water is
at we want to make sure we are always
reading the bottom one
and remember this graduated cylinder is
marked for every milliliter so our
estimate comes in the tenths place
in this case i can see that the water is
past
52 milliliters but the bottom of the
meniscus has not quite made it to 53
milliliters yet
so i would call this one 52.8 or 52.9
milliliters
in this graduated cylinder the meniscus
is much easier to see
because it's a narrower graduated
cylinder
again we read all the digits we know for
certain we know that it is past
eight milliliters and i noticed that
each
tenth of a milliliter is marked on this
graduated cylinder so i know that
position for certain as well
i can see that it is past the
third mark so it's at least 8.3
again reading the bottom of the meniscus
it's not quite
to 8.4 yet so i would read this
as 8.3 8 or 8.37
milliliters the last device we're going
to look at in this video is a meter
stick or a ruler
for a meter stick or a ruler
it measures typically in centimeters so
each mark is a centimeter
when you zoom in you will see millimeter
marks or tenth of a centimeter
let's take a look and measure the length
of an index card
i make sure to line up the end of the
meter stick
with the index card because in this case
zero is right at the end
some ruler zero is offset so you'll have
to be careful on how you line that up
you can see that every tenth of a
centimeter is marked so we know that
digit for certain
our estimate comes in the hundredth of a
centimeter i'm going to zoom a little
further in so we can see a little more
clearly
we know that it is at least 12
centimeters
in this case i can count that it is past
12.6 centimeters
very close to 12.7 so the length of this
index card is about 12.68 centimeters
[Music]
浏览更多相关视频
5.0 / 5 (0 votes)