Chemistry Lesson: Introduction to Measurements

Summary

Dr. 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

00:00

🔍 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.

05:01

📏 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.

10:02

🔢 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.

15:02

🌡️ 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.

Keywords

💡Measurement

Measurement refers to the process of determining the value of a physical quantity, such as length, temperature, or weight, using a device or instrument. In the video, Dr. Kent emphasizes the importance of recording both the number and a unit when making scientific measurements, as it provides context and meaning to the data collected. For instance, the script mentions measuring the length of a rod and recording it as '52.8 kilometers' or '52.8 degrees Fahrenheit,' which would require a unit to be scientifically meaningful.

💡Unit

A unit is a standard of measurement that defines the magnitude of a physical quantity. In the context of the video, Dr. Kent highlights that every measurement must be accompanied by a unit to be scientifically valid. Units are crucial for understanding and comparing measurements, as they specify what the number represents, such as 'kilograms' in the case of mass or 'meters' for length.

💡Exact Numbers

Exact numbers are values that are defined to be true or obtained through counting, without any ambiguity or estimation. In the video, Dr. Kent explains that exact numbers are not subject to error, such as 'one dozen' being exactly 12, or 'one week' being exactly seven days. These are used to contrast with inexact measurements, which involve some degree of approximation.

💡Inexact Numbers

Inexact numbers, as discussed in the video, are those obtained through measurement and are subject to some degree of estimation or approximation. Dr. Kent gives examples like body temperature or weight, which are measured and thus can only be approximated rather than defined exactly. These numbers are always associated with some error.

💡Accuracy

Accuracy in the context of the video refers to how close a measurement is to the true or accepted value. Dr. Kent uses the analogy of a target to illustrate that accuracy is about hitting the 'bullseye' or being correct in one's measurement. It is a critical aspect of scientific measurements, as it determines the reliability of the data collected.

💡Precision

Precision is defined as the consistency or closeness of a set of measurements to one another. In the video, Dr. Kent explains that precision is about the repeatability of measurements; a precise set of data will have values that are clustered closely together, indicating a low degree of variability. Precision is distinct from accuracy, as a measurement can be consistent but still not reflect the true value.

💡Error

Error in the video script refers to the difference between a measured value and the true value. Dr. Kent discusses that all measurements have some degree of error, and the goal in scientific measurements is to minimize this error. The concept of error is closely tied to the precision of a measurement, with more precise measurements indicating less error.

💡Significant Figures

Significant figures, as explained by Dr. Kent, are the digits in a number that carry meaning contributing to its precision. They include all the known digits plus one estimated digit. The number of significant figures indicates the level of precision and the amount of error in a measurement. For example, the measurement '4.25 cm' has three significant figures, suggesting a higher precision than '4.2 cm' which has two.

💡Estimation

Estimation in the video is the process of approximating a value beyond what is directly measured. Dr. Kent illustrates that when recording a measurement, one should estimate one digit beyond the last clearly marked value on the measuring device. This estimated digit represents the uncertainty in the measurement and is a part of determining significant figures.

💡Graduated Cylinder

A graduated cylinder is a piece of laboratory equipment used for measuring the volume of liquids. In the video, Dr. Kent uses the example of a graduated cylinder to demonstrate how to record measurements with the correct number of significant figures. The cylinder is marked with gradations, and the user estimates the volume to the next smallest division beyond what is clearly visible.

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