1.2 Scientific Notation & Significant Figures | General Chemistry
Summary
TLDRThis 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
🔢 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.
📏 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.
🔄 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.
➕➖➗ 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.
🎯 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.
Mindmap
Keywords
💡Scientific Notation
💡Significant Figures (Sig Figs)
💡Precision
💡Accuracy
💡General Chemistry
💡MCAT and OAT
💡Decimal Place
💡Powers of 10
💡Zero Rules
💡Mathematical Operations
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
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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
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