1.2 Scientific Notation & Significant Figures | General Chemistry

Summary

This chemistry lesson with Chad focuses on scientific notation and significant figures, essential for handling large or small numbers in chemistry. Chad explains scientific notation's convenience and its use with large and small numbers, emphasizing the importance of significant figures in determining the precision of a number. He illustrates the rules for counting significant figures, including zeros, and covers mathematical operations like multiplication, division, addition, and subtraction with respect to significant figures. The lesson concludes with a distinction between precision and accuracy, crucial for understanding measurement reliability in science.

Takeaways

• 🔢 Scientific notation is a method used to simplify the writing of very large or very small numbers by expressing them as a product of a number between 1 and 10 and a power of 10.
• 📉 For large numbers greater than 1, scientific notation uses positive powers of 10, whereas for numbers less than 1, it uses negative powers of 10.
• 📝 In scientific notation, a number should be written with a single digit to the left of the decimal point, followed by the appropriate power of 10.
• 🔑 Significant figures (sig figs) represent the precision of a number, indicating how well the number is known.
• 🌐 The number of significant figures in a measurement affects the precision of the final result when performing calculations.
• 🚫 Any zeros at the beginning of a number are not considered significant figures.
• ✅ Zeros between significant figures are always significant, as they contribute to the precision of the number.
• ➡️ When performing multiplication and division, the number of significant figures in the result is determined by the number with the least significant figures.
• 🔄 For addition and subtraction, the final answer's precision is limited by the least precise number in the calculation, which is determined by the position of the last significant digit.
• 🧪 In laboratory settings, maintaining proper significant figures is crucial as incorrect handling can lead to significant errors in scientific and engineering applications.
• 🎯 The difference between precision and accuracy is important to understand; precision refers to the repeatability and closeness of multiple measurements to each other, while accuracy is about how close the measurements are to the true value.

Q & A

What is scientific notation and why is it used in chemistry?

Scientific notation is a method of expressing very large or very small numbers in a compact form using powers of ten. It simplifies calculations and standardizes the way numbers are written, especially useful in chemistry where numbers can span a wide range of magnitudes.

How do you express a large number in scientific notation?

To express a large number in scientific notation, you place the decimal after the first non-zero digit and multiply by 10 raised to the power of the number of places the decimal has moved. For example, 472,000 becomes 4.72 x 10^5.

What is the proper form for writing a number in scientific notation?

A number in proper scientific notation should have a single digit to the left of the decimal point and can be followed by any number of digits to the right. It is then multiplied by 10 raised to the appropriate power.

What happens to the power of 10 when dealing with numbers smaller than one in scientific notation?

When dealing with numbers smaller than one, you use negative powers of 10 in scientific notation. This indicates that the decimal point has been moved to the right to make the number larger.

How are significant figures abbreviated and what do they represent?

Significant figures, abbreviated as 'sig figs', represent the precision of a number, indicating how well you know the number. They count all non-zero digits, zeros between significant figures, and trailing zeros in a decimal.

Why are significant figures important in the sciences?

Significant figures are important because they convey the reliability of a measured value. They ensure that calculations reflect the precision of the original measurements, preventing false accuracy.

How do you determine the number of significant figures in a number?

Count all the digits starting from the first non-zero digit on the left to the last digit on the right, including zeros that are between non-zero digits or trailing zeros in a decimal number.

What are the rules for determining when zeros are significant in a number?

Zeros are significant if they are: 1) between non-zero digits, 2) after a decimal point and to the right of non-zero digits, or 3) in a number expressed in scientific notation.

How does the number of significant figures affect calculations?

The number of significant figures affects calculations by determining the precision of the result. When multiplying or dividing, the result can only have as many significant figures as the least precise number in the calculation. For addition or subtraction, the final answer's precision is limited by the least precise number's least significant digit.

What is the difference between precision and accuracy as discussed in the script?

Accuracy refers to how close a measurement is to the true value, while precision refers to the repeatability or consistency of measurements. A measurement can be precise (consistent) but not accurate (not close to the true value), and vice versa.

Outlines

00:00

🔢 Scientific Notation Explained

The paragraph introduces scientific notation as a method for conveniently writing very large or very small numbers, which are common in general chemistry. The instructor, Chad, explains how to convert a regular number into scientific notation by moving the decimal point so that only one non-zero digit lies to the left of the decimal. For large numbers, this involves using positive powers of 10, while for small numbers, negative powers are used. The proper format for scientific notation is also emphasized, where the number should have a single digit before the decimal point, followed by the appropriate power of 10.

05:01

📏 Understanding Significant Figures

This section delves into significant figures (sig figs), explaining their importance in representing the precision of a measurement. Chad uses the example of estimating the distance from Phoenix, Arizona to Portland, Maine to illustrate how the number of significant figures affects the precision of the distance. The paragraph clarifies that significant figures indicate how well we know a number, with zeros in certain positions being significant and others not. The rules for determining the significance of zeros are also outlined: zeros at the beginning of a number are never significant, while those at the end (to the right of the decimal) are significant if they indicate a precise measurement.

10:02

🔄 Rules for Significant Figures in Calculations

The paragraph discusses the rules for determining significant figures when performing mathematical operations. It emphasizes that in multiplication and division, the number of significant figures in the result cannot exceed the number present in the least precise number of the operands. An example is given where two numbers with different numbers of significant figures are multiplied, and the result is rounded to the number of significant figures of the least precise number. The concept is further explained with an addition example, where the final answer's precision is limited by the least precise term, aligning with the place value of the least precise number's significant figure.

15:03

➕➖➗ Mathematical Operations and Sig Figs

This part of the script continues the discussion on mathematical operations, focusing on how to handle significant figures when adding and subtracting numbers. It points out that while multiplication and division maintain significant figures at the end of the calculation, addition and subtraction require adjusting the number of significant figures based on the precision of the least precise number. An example calculation is provided, showing how to round the sum to match the precision of the least precise term before proceeding with further operations like division.

20:03

🎯 Precision vs. Accuracy

The final paragraph distinguishes between precision and accuracy, two terms that are often used interchangeably but have distinct meanings in scientific and engineering contexts. Accuracy refers to how close a measurement is to the true value, while precision indicates the repeatability or consistency of measurements. Chad uses a bullseye analogy to illustrate the difference: a precise set of measurements would cluster closely together, even if not near the true value, whereas an accurate set would hit near the center of the target. The paragraph concludes with an encouragement for students to engage with the material and ask questions, highlighting the practical importance of understanding significant figures and the difference between precision and accuracy.

Keywords

💡Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is commonly used in science and engineering to simplify calculations and data presentation. In the video, scientific notation is introduced as a method to handle very large or very small numbers encountered in general chemistry, such as the size of atoms or the number of molecules in a sample.

💡Significant Figures (Sig Figs)

Significant figures refer to the digits in a number that carry meaning contributing to its precision. This concept is crucial in scientific measurements to indicate the reliability of the data. The video emphasizes the importance of understanding how many significant figures a number has and how this affects calculations, which is particularly important in lab work and scientific computations.

💡Precision

Precision in the context of the video refers to the degree of repeatability or consistency of measurements. It does not necessarily imply that the measurements are close to the true value, but that they are close to each other. This is a critical concept in scientific experiments where consistent results are often more valuable than a single accurate measurement.

💡Accuracy

Accuracy, as discussed in the video, is the closeness of a measured value to the true or actual value. It is distinguished from precision in that accuracy is about being correct, whereas precision is about being consistent. The video uses the analogy of a bullseye to illustrate the difference between precision and accuracy.

💡General Chemistry

General chemistry is a foundational course in chemistry that covers basic concepts and principles. The video is part of a series designed to help students understand and master topics in general chemistry, such as scientific notation and significant figures, which are fundamental to the scientific method and calculations.

💡MCAT and OAT

MCAT (Medical College Admission Test) and OAT (Optometry Admission Test) are standardized exams for admission to medical and optometry schools, respectively. The video mentions that the channel also provides preparation for these tests, indicating that the concepts of scientific notation and significant figures are not only essential for general chemistry but also for professional entrance exams.

💡Decimal Place

The decimal place is an important aspect of scientific notation and significant figures discussed in the video. It refers to the position of digits relative to the decimal point in a number. Proper scientific notation requires that there be only one digit to the left of the decimal point, and the video explains how to adjust numbers to meet this requirement.

💡Powers of 10

Powers of 10 are used in scientific notation to express very large or very small numbers. The video explains how to move the decimal point in a number to the right position and then express the number as a product of a coefficient and a power of 10. This concept is essential for simplifying the writing and manipulation of large or small numbers in scientific calculations.

💡Zero Rules

The video provides specific rules regarding zeros in the context of significant figures. It explains that zeros at the beginning of a number are not significant, zeros at the end of a number (to the right of the decimal point) are significant, and zeros in the middle of a number (surrounded by other significant figures) are significant. Understanding these rules is crucial for accurately determining the precision of a measurement.

💡Mathematical Operations

The video discusses how to perform mathematical operations such as multiplication, division, addition, and subtraction while maintaining the correct number of significant figures. These operations are fundamental to chemistry and other scientific disciplines, and the video provides guidelines on how to apply the rules of significant figures to these calculations.

Highlights

Scientific notation is introduced as a method for writing very large or very small numbers conveniently.

Scientific notation simplifies writing numbers by moving the decimal point and using powers of ten.

For large numbers, scientific notation uses positive powers of ten.

For small numbers, scientific notation uses negative powers of ten.

The significance of scientific notation in general chemistry is highlighted.

The concept of significant figures (sig figs) is introduced as a measure of the precision of a number.

Sig figs are important in science and engineering to ensure accurate calculations.

The difference between significant and non-significant zeros is explained.

Zeros at the beginning of a number are never significant.

Zeros at the end of a number are significant if they are to the right of the decimal point.

Zeros in the middle of a number are significant if they are between non-zero digits.

Scientific notation ensures all zeros are significant as they must be placed after the decimal point.

Rules for determining significant figures in multiplication and division are discussed.

In addition and subtraction, the precision of the least precise number dictates the final answer's precision.

The importance of sig figs in laboratory work is emphasized.

The difference between precision and accuracy is explained using the analogy of a bullseye.

Accuracy is defined as how close a measurement is to the true value.

Precision is defined as the repeatability or closeness of multiple measurements to each other.

Transcripts

scientific notation and significant

figures in this lesson we're going to

take a look at a couple of common ways

we treat numbers in general chemistry my

name is chad and welcome to chad's prep

where my goal is to take the stress out

of learning science this lesson is part

of my new general chemistry playlist

i'll be releasing these weekly

throughout the school year so if you

want to be notified every time i post a

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click the bell notification in addition

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all right so we're going to start with

scientific notation here and scientific

notation is just a really convenient way

of writing either very large or very

small numbers and that's something we

run into quite commonly in general

chemistry so when you're dealing with

like the size of an atom being like a

fraction of a nanometer that's a really

small fraction of a meter uh you're

dealing with really small numbers or

because they're so small if you're

dealing with the size of a sample that

you know fits in the palm of your hand

you've got such a huge number of either

atoms or molecules there that you're

going to be dealing with very large

numbers and writing really small and

really large numbers can be a pain in

the butt but we can make it much simpler

with scientific notation

way this works

so we'll start with a large number here

and we've got a decimal that's not

written that's essentially right there

and in this case we're going to move

that

until we've got just one number left of

the decimal place now we can write a

number in scientific notation with more

than one number left of the decimal

place but that's not proper

properly it should be written with just

a single digit left of that decimal and

so we'll rewrite this here as 4.72

so and then we moved it one two three

four five places so in this case that's

going to be times 10 to the fifth power

way this works is when you've got large

numbers numbers that are much larger

than one you're going to end up with

positive powers of 10 but we'll see over

here when we've got numbers that are

smaller than 1 we're going to end up

with negative powers of 10.

so for this one here we're going to move

the decimal now to the right instead one

two

three places and this is going to become

7.349 9. notice we've got just one digit

left of the decimal as is proper for

scientific notation and then times

10 to the power of and in this case it's

going to be

negative 3. we moved it three places but

again for a number that's much less than

one it should be a negative power of 10.

so and these are equivalent expressions

for the same number as are these two

right here and so a couple different

ways you can look at it one again if

you've got a number much bigger than one

positive powers of 10 number much

smaller than one negative powers of 10

so other way to look at this is if

you're taking this number and if you're

making this number smaller notice went

from 472 000 to now a coefficient of

4.72 so then you better have a very

large power of 10 to make it uh to make

up for it so because it's got to be the

same number so if your number part gets

smaller your power of 10 better get

bigger same thing over here in this case

we made a very small number 0.007349

get bigger to 7.349 and so if the number

gets bigger your power of 10 better gets

smaller in this case cool this is as

much of scientific notation as i want to

cover right now

but basically i want to give an

introduction first because this is going

to be helpful when we start talking

about significant figures

so now we've got to talk about

significant figures or sig figs for

short and significant figures a lot of

students memorize the processes of how

we determine how many sig figs and how

we do certain mathematical operations

but they never kind of understand why

we're even doing this and but

significant figures deal with how well

do we really know a number how precisely

do we really know a number and so let's

say we take a look here and i'm right

here in phoenix arizona and let's say

i've got my friend up here in

portland

maine

so

and somebody asked me hey how far is it

to your friend up in portland maine and

i say well you know it's about

it's 3000 miles

so and in this case like you know that's

a pretty rounded number you know it's

exactly 3000 miles like to the you know

to the t

or or is it like you know give or take

well you know if i had to round it to

the nearest thousand

it'd be about three thousand miles

that's a better approximation than two

thousand or four thousand so that's kind

of the deal but it's not you know not

that exact in this case

and so in this case

you know with significant figures we

often look at zeros as not being

significant

uh as the case would be in so this would

have one significant figure in the

thousands place and be you know as

precise as it is to plus or minus a

thousand so to speak all right so what

if i said actually it's like 2700 miles

well this makes a big difference you

know in a lot of vehicles this would be

the difference between a full tank of

gas and getting there or something like

this so all of a sudden now i've got a

more precise number and it's got

significant figures now

in both the thousands and the hundreds

place and so now this number would

actually be considered to be precise

like plus or minus a hundred

so maybe that's where we go maybe take

this a step further and actually go and

say hey it's actually 20

2740

miles

to my friend's house in portland maine

okay so looking at that now and all of a

sudden now we've got significant figures

in the thousands hundreds and tens place

so and again that zero is not going to

be significant it turns out but the way

we look at this is now it is exact or

precise all the way to plus or minus 10

miles so much more precise now and

finally if if i take this you know to

the certain extent i go it's 2739.1

miles and all of a sudden now i've got a

very precise number relative to the

numbers we've given before and it's

precise all the way to the tenths place

on the other side of the decimal so we'd

say this has five significant figures

and now the sudden it's just a much more

precise number and this is important you

know if you're dealing with the sciences

or engineering or something like that

say you're building a bridge so and you

start using you know rounded

approximations on setting up uh you know

some of the supports on your bridge and

you know because you're rounding to such

a great extent maybe your bridge is not

as strong as you think it is or

something like this and so this is where

the significant figures become important

it's how well do you really know your

numbers and when you start doing

calculations with them there's way of

ways of propagating these significant

figures so that you know

how much of whatever you should be doing

or how much of whatever you should be

adding so when it comes to chemistry and

stuff like this so but this really is

important for science and engineering so

for you and your general chemistry

course you're just going to need to know

how uh you know how to process you know

determine how many sig figs and how to

do uh say addition subtraction

multiplication division and stuff like

this so but this really does have real

world importance although that might get

lost on you in your course uh however

this is something you do need to know it

is commonly uh questions on your first

round of exams and stuff like this uh

and it's also really important in the

laboratory most professors and

instructors are going to really ding you

on sig figs if you're not doing it

properly in the laboratory so

all right so let's take a closer look

here at sig figs

all right so the first thing i'm going

to deal with with significant figures

are the zeros so

any numbers that are non-zero are going

to be significant and the pesky little

things are the zeros sometimes they're

significant and sometimes they're not

we've got some rules for this and

so the first rule is if your number

starts off with zeros those zeros are

never significant so here we've got zero

point zero zero zero four seven and the

number starts off with all zeros so in

this case those zeros are not

significant and as a result this first

number only has two significant figures

the four

and the seven so it's got a significant

figure here in the one so notice this is

the tenths hundredths thousandths in the

ten thousandths place and the hundred

thousandths place that's where the

significant figures are

so

any zeros at the beginning of a number

never significant now notice like this

next number 40 5400 we'll deal with that

in a second

so

but let's say i had 5400 and i just put

a couple zeros on the front of it well

we'd never do that but if we did they

wouldn't be significant either so just

want to point out that zero is the

beginning of a number it doesn't matter

where you know which side of the decimal

place they are on are not going to be

significant and in one case we wouldn't

even write them so and the reason that

becomes important is because now zero's

at the end of a number sometimes they're

significant and sometimes they're not

and so it turns out when you end a

number in zeros

so but it's to the left hand of the

decimal and often the decimal wouldn't

even be written notice there's an

imaginary decimal right there so those

zeros are not going to be significant

either and so here we've also only got

two significant figures these zeros are

not

significant in this case and that's

going to be different than what we see

in the next example because if you end a

number in zeros but it's to the right

hand side of the decimal those zeros are

going to be important so not only are

the the two the five and the four

significant but these two zeros are

significant as well and this is a way of

saying that you know we know this number

really really well so

2.5400 it's really precise how well we

know this number to the right of the

decimal here but this is like you know

it's about 5 400 miles give or take 100

and stuff like this so however what if

it really was like

5400 miles to the nearest mile and you

actually meant it like you look it up on

google and it was exactly 5400 to the

nearest mile

well the way we might show that

in such a case to show that it's

significant there's really two ways

we might put a line across the top of

that zero which is going to show that

it's significant that might be one way

to do it so

and that gets to be a little bit of pain

in the butt so however

another way to pull this off is to use

scientific notation so if we really did

mean 5400 exactly all the way to plus or

minus one mile here all the way to the

single digits place here then what we

could do is convert this to scientific

notation and make it five point four

zero zero

times ten in this case we moved it one

two three ten to the third and it's a

positive power 10 because we're dealing

with a number that's bigger than one

and in this case notice now these zeros

are to the right of the decimal and if

you end a number and zeros right at the

decimal they're significant and so now

we have our four sig figs and so what's

nice about scientific notation

is that

you know

all of your

zeros and stuff like that are always

going to be significant because if

you're in proper scientific notation you

have to have a number left of the

decimal not zero so you can't even start

a number with zeros like we did right

here and if you ever do have zeros

they're always going to be right of the

decimal so they're always going to be

significant so that's one thing that's

nice about scientific notation is

all of your numbers are always

significant now the last rule dealing

with zeros is that zeros in the middle

of the number are always significant and

so in this case what i really should

properly say is that zeros that are

surrounded by significant figures so

that two is significant the one and the

six are significant and zeros that are

in between other significant figures are

themselves significant

so in this case we'd have five

significant figures in 200.16

cool and those are your rules so again

zero is the beginning of a number never

significant zeros at the end are

significant if they're right of the

decimal not significant if it's left of

the decimal and then zeros in the middle

of your number surrounded by significant

figures are also significant so that's

your rules for zeros and you've got to

be able to kind of identify when zeros

are and are not

significant but you've also got to be

able to do some basic mathematical

operations you've got to be able to do

multiplication and division which is by

far the most common mathematical process

you'll do in general chemistry but you

might also have to do a little bit of

addition and subtraction and it turns

out so for propagating like number of

sig figs and stuff there's rules for

logs and other mathematical processes

that just aren't going to probably come

up in your general chemistry course so

but multiplication subtract i'm sorry

multiplication division for sure and

addition subtraction probably and so

we're going to cover those here next

so we're going to start with

multiplication and division and and in

general chemistry that's by far the most

common operation you're going to do and

have to determine significant figures

for it's the easier of the two as well

and so the way this works in every term

you're multiplying and dividing if all

you're doing is multiplying and dividing

a big string of numbers then you can do

this all at once at the end you don't

have to do it every step along the way

and so in this case i've just got two

numbers but what if i was multiplying

like four numbers in a row well then you

just count how many sig figs you had in

each number i'm going to do that here so

this first one's got three sig figs the

second one's got

four sig figs so and it turns out that

your answer if all you're doing is

multiplying and dividing can't be more

precise than your least precise number

so to speak and so in this case your

whichever of your numbers has the lowest

number of sig figs your answer can only

have that number of sig figs so here one

of my numbers has got three sig figs

one's got four my answer's only gonna be

able to have three sig figs and if we

work this out we're gonna get 17.97

and so i'm going to carry this to four

sig figs so but then i'm going to take

this last one right here

and use it to round the one right before

it's that we end up with a final answer

and only three sig figs in this case

that seven is going to cause us to round

up and in this case that's gonna take

this to 18.8

and that zero ends the number right hand

side of the decimal so it is significant

and we've now got three sig figs there

in 18.0 and that would be the answer

here in the proper number of sig figs

and the idea is that you know if you're

multiplying a string of numbers and if

you know some of them very well very

precisely with lots of sig figs but one

of them is really much more approximate

well again you can only be as exact as

your least exact or least precise number

that's kind of the way it works and

we'll see the a similar fashion when

we're doing addition and subtraction

here now you're going to do addition and

subtraction much

less commonly um but it is going to show

up every once in a while because it

shows up so uncommonly a lot of students

forget there's even a different process

and they try to do the same thing they

do for multiplication division but with

an addition and subtraction the way this

works so i'd recommend adding these up

kind of the way you did back in grade

school so line them up a little bit

differently so we're going to have 1500

plus 327.4

plus 0.267

and so if you look at these numbers so

this one your most exact digit here is

this seven all the way down here in the

thousandths place and so we know this

number plus or minus one one thousandth

so for this one it's all the way to the

tenths place we know this number plus or

minus one tenth so and then 1540 here is

only exact its most precise significant

figure is that four that zero is not a

significant figure and so in this case

it's in the tens place and so it's only

exact or precise to plus or minus 10.

and so it turns out your final answer

when you add all these together

can't be more precise than your least

precise digit so

in a way actually i've got it right on

the sheet there in this case i say the

answers round to the same decimal place

as the most precise decimal place in the

least precise term and so in this case

this is the least precise term and its

most precise decimal place is in the

tens place and so in this case we're

gonna have to round whatever this comes

out to to the tens place with addition

abstraction so it's not about counting

how many sig figs this has got three and

this has got four and this got three so

we should have three sig figs it's not

how it works it's actually you have to

look at how precise each individual

number is in the least precise number

that's as precise as your final answer

can be and so if we work this out now so

1540 plus

327.4

plus

0.267

equals 1867.6

and truth be told i didn't actually have

to carry it any farther than right here

because i need to use this digit to

round it to the tens place

and so in this case this is going to

round to

1870. the seven means we round up

and there's our correct answer and

notice it just happens to have three sig

figs but it's not because we needed to

make sure it had three sig figs it's

exactly where it's at because we needed

to make sure that the most

precise

significant figure was in the tens place

based on the numbers that were given

okay now this is the last part here is

going to show up much less commonly

than any of the rest and here we've got

both multiplication and division and

addition and subtraction and you've

actually got to propagate your your

proper number of sig figs all along

the way and so you want to follow your

order of operations here and stuff like

this and notice we're going to have to

add these before we actually divide the

sum of those two by 0.5 and when we add

these we're then going to have to adjust

the number of sig figs and then when we

divide by the bottom number we'll then

go to go further and adjust the number

of sig figs yet again

and so oh and i lost a zero there's a

zero on your hand out so that lost a

zero right there that way we got two sig

figs in that number not just one all

right so 4.23 plus 7.6

is 11.83

so problem is is that here i haven't

adjusted my sig figs to take into

account the numbers we have and when

addition and subtraction i can see that

this first number is significant all the

way to the hundredths place but the

second number is only significant to the

tenths place and so i'm going to have to

round it to the tenths place and i'll

use the number right after in this case

being a three i'm just going to keep it

as a point eight i'm around down here so

we can essentially just get rid of that

three

to get it now only significant to that

tenths place and now we've got to do the

process of division

and so we'll take 11.8

divided by 0.5 and get 23.6

in this case with doing multiplication

division in this case typically division

now it's all about the number of sig

figs in the numerator i've got three

significant figures in the denominator

i've only got two and so my final answer

should only actually have two sig figs

and so we want to round it here at the 3

and so that 6 is going to cause it to

round up and so the actual final answer

here

is 24.

like i said you know having to do both

addition subtraction and multiplication

division in the same problem doesn't

show up too often but it does have a

chance of showing up right here in this

first

chapter now one thing to note about sig

figs is that with sig figs we're gonna

make a real big point of it in this

chapter and on the exam

for this section however much of the

rest of the semester it is not going to

be the biggest deal sort of and what i

mean by that is that you're probably not

going to have a bunch of multiple choice

answers after this test anyways

and maybe not until your final exam

anyways as well but on you know second

third and fourth exam you're probably

not going to have a bunch of multiple

choice answers that you know have just

the same answer especially in a

different number of sig figs it's not

usually how it works so

it's not going to have the same level of

importance the rest of the semester at

least not until the final exam as it

does on this first test but once again

don't forget that in the laboratory sig

figs is typically a pretty big deal for

most professors and instructors so

even though it's not going to get a huge

focus in the course

after this first exam keep in mind it's

still got a huge focus in the lab

all right we're going to finish this

lesson off with a really brief

discussion of precision versus accuracy

and it's important because precision and

accuracy in the everyday vernacular we

kind of use them interchangeably so but

in the sciences and engineering they

actually have uh

similar related meanings but they are

distinct and you definitely need to know

the difference and so it turns out

precision is not what you'd think a lot

of people think that again in everyday

life we treat precision as if it's just

the same thing as accuracy and let's

talk about accuracy first accuracy is

how close to the true value

you are that's it so but precision is

different it's not about being right so

to speak uh but it goes more to the

repeatability of a measurement if you

will and it's how close

multiple different independent

measurements are to each other

not to the true value that's what

precision deals with and again it gets

down to the repeatability of it so

and again in chemistry we're probably

going to you know

get this in the context of measuring the

weight of something or measuring the

volume of something or something along

those lines but it's often really

convenient to look at

a diagram of a bullseye here

for the way this works and so if i was

testing out a new bow and arrow so

and if i shot four shots and they all

were right in the bull's-eye right there

well one we'd say that in this case this

bow was very accurate because i was

hitting the the place where i was hoping

to hit right in the bullseye but we'd

also say it's very precise because all

four of the arrows are close together

we'd call this a good grouping in

archery

so this would be both precise and

accurate now on the other hand if i

tried out that same bow and

unfortunately instead of hitting the

bullseye in the middle here

i hit four arrows right here well that's

still

a rather close grouping so but maybe you

know maybe the sight on the uh on the

bow is off or something like this

because even though it was very

repeatable which makes it very precise

it was not very accurate because i

didn't come close to the bull's-eye and

so this would be an example of something

that's very precise but not accurate

and then finally here i'm just all over

the board i'm not close to the bullseye

but none of the arrows are particularly

close to each other and so this is

neither precise

nor

accurate

cool

so hopefully this demonstrates well that

difference between precision and

accuracy and once again accuracy is how

close you are to that true value but

precision is how close the values are to

each other but not necessarily uh to

that true value they can be close to

that true value but they don't have to

be close to that true value they can

still be precise in either case now if

you found this lesson helpful and think

other students would benefit from seeing

it as well consider giving me a like and

a share best thing you can do to make

sure it gets as wide an audience as

possible and if you've got questions

involving either sig figs or scientific

notation or precision versus accuracy

feel free to leave them in the comments

section below happy studying