Significant Figures and Measurement

Summary

This 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

00:00

🔍 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.

05:02

🧪 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.

10:03

📏 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.

15:04

📏 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.

Keywords

💡Significant Figures

Significant figures refer to the digits in a number that carry meaning contributing to its precision. In the video, significant figures are crucial for accurately reporting measurements. The definition provided is 'all digits that we know for certain, plus one uncertain or estimated digit.' This concept is applied when reading different measuring devices, ensuring that the measurements are reported to the correct level of precision. For example, when using a triple beam balance, the measurement is reported with significant figures in mind, such as 56.62 grams, where '56.6' is certain and '2' is the estimated digit.

💡Accuracy

Accuracy in the context of the video is the closeness of a measured value to the true or correct value. It is a fundamental aspect of measurement that the video aims to improve. The script mentions that accuracy is about how close the measurement is to the 'correct number,' which is essential for reliable scientific experiments and results. The video demonstrates how to achieve accuracy through the proper use of measuring instruments and the consideration of significant figures.

💡Precision

Precision is the degree of repeatability or consistency of measurements. It is highlighted in the video as a key component of measurements, distinct from accuracy. Precision is about how closely multiple measurements can be repeated under the same conditions. The video script discusses precision in relation to the use of different measuring devices, emphasizing the need for consistent and repeatable measurements to ensure reliable results.

💡Measurement

Measurement is the process of determining the value of a quantity, such as length, mass, or volume. The video script revolves around the concept of measurement, showing how to use various tools to accurately and precisely measure different properties. Examples include using a triple beam balance to measure mass or a graduated cylinder to measure volume. The video provides detailed instructions on how to perform these measurements, emphasizing the importance of significant figures in reporting the results.

💡Triple Beam Balance

A triple beam balance is a type of scale used for measuring mass. In the video, it is used as an example of a device that requires calibration and the understanding of significant figures for accurate mass measurements. The script describes the process of calibrating the balance and then using it to measure the mass of an object, such as a roll of tape, with an example measurement of 56.62 grams, illustrating the application of significant figures.

💡Calibration

Calibration is the process of adjusting a measuring instrument to ensure it provides accurate and consistent results. The video script discusses the importance of calibration for devices like the triple beam balance, where the calibration knob is adjusted until the balance is level. Proper calibration is essential for reliable measurements and is a critical step demonstrated in the video before taking any measurements.

💡Graduated Cylinder

A graduated cylinder is a piece of laboratory equipment used for measuring the volume of liquids. The video explains how to read a graduated cylinder, which is marked for every milliliter, and how to estimate the volume to the nearest tenth of a milliliter. The script provides a practical example of measuring 50 milliliters of liquid, demonstrating the process of pouring, leveling, and reading the meniscus to determine the volume.

💡Meniscus

The meniscus is the curved surface of a liquid in response to its container, which affects how the volume is read in a graduated cylinder. The video script describes the importance of reading the bottom of the meniscus when measuring liquid volumes to ensure accuracy. It is a critical concept when using a graduated cylinder, as it directly impacts the precision of the volume measurement.

💡Estimation

Estimation in the context of the video refers to the process of approximating a value that is not exactly marked on a measuring instrument. The script explains that each measurement must include an estimate, which is the last significant figure in a measurement. For instance, when measuring mass with a balance, the last digit is an estimate, allowing for slight variation in the reported value, such as 56.62 grams where '2' is the estimated digit.

💡Ruler

A ruler, or meter stick, is a tool used for measuring length or distance. The video script includes an example of using a ruler to measure the length of an index card, demonstrating how to align the ruler with the object and read the measurement to the nearest hundredth of a centimeter. The ruler is marked for every centimeter and tenth of a centimeter, which is important for understanding the precision of the measurement.

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]