Significant Figures - A Fast Review!
Summary
TLDRThis video script offers an educational overview on significant figures, explaining how to identify and count them in various numerical formats. It clarifies the significance of zeros, both leading and trailing, and provides examples to illustrate the concept. The script also covers rounding rules for multiplication and division, emphasizing the importance of adhering to the least number of significant figures in the original numbers. Practical examples are given to demonstrate these principles, and viewers are encouraged to practice with a quiz and additional resources provided in the video description.
Takeaways
- 🔢 Significant figures are the digits in a number that carry meaning contributing to its precision.
- 📐 Every non-zero digit is considered a significant figure, as seen in the number 846 which has three significant figures.
- 🌀 Zeros between non-zero digits are significant, making 704 have three significant figures and 5006 have four.
- 📉 Trailing zeros to the right of a non-zero number are not significant unless there is a decimal point, as in 500.0 which has four significant figures.
- ❌ Leading zeros, such as those in 0.075, are never significant, leaving only the digits seven and five as significant in this case.
- 📌 The presence of a decimal point affects the significance of trailing zeros, making them significant and contributing to the total count of significant figures.
- 📝 When performing multiplication or division, the final answer should be rounded to the least number of significant figures found in the original numbers.
- ➗ In division, the final answer should be rounded to the least number of significant figures between the dividend and the divisor.
- 🔄 For addition and subtraction, the final answer should be rounded to the least number of decimal places found in the numbers involved.
- 📉 Leading zeros in a number are not counted as significant figures, as in 0.00836 where only the digits eight, three, and six are significant.
- 📈 The video provides examples and a quiz to help viewers practice determining the number of significant figures in various numbers.
- 🔗 Additional resources and a more in-depth video on significant figures are available for those who wish to explore the topic further.
Q & A
What is the definition of significant figures?
-Significant figures are the digits in a number that carry meaning contributing to its precision. This includes all the non-zero digits, any zeros between significant digits, and any trailing zeros in a decimal number.
How many significant figures are in the number 846?
-The number 846 has three significant figures because every non-zero digit is significant.
Are the zeros between non-zero digits in the number 704 considered significant?
-Yes, all zeros between two non-zero numbers are significant, so 704 has three significant figures.
What about the zeros to the right of a non-zero number without a decimal point, like in 500?
-Zeros to the right of a non-zero number without a decimal point are not significant, so 500 has only one significant figure.
How many significant figures does the number 500.0 have?
-The number 500.0 has four significant figures because the presence of the decimal point makes all trailing zeros significant.
Are leading zeros in a number like 0.075 ever significant?
-No, leading zeros are never significant, so there are only two significant figures in 0.075: the seven and the five.
In the number .0050830, how many significant figures are there?
-There are five significant figures in .0050830 because the leading zeros are not significant, but the zeros between non-zero digits and trailing zeros after the decimal point are.
What is the correct way to round a number when multiplying or dividing?
-When multiplying or dividing, round the final answer to the least number of significant figures found in the original numbers used in the calculation.
How many significant figures should the result of multiplying 4.6 by 3.52 have?
-The result should have two significant figures, which is the least number of significant figures between the two original numbers.
How many significant figures are in the number 42.50?
-The number 42.50 has four significant figures, including the trailing zero because of the decimal point.
When adding numbers like 2.36 and 12.1, how should you round the final answer?
-When adding or subtracting, round the final answer to the least number of digits to the right of the decimal point in the numbers involved.
What is the final rounded result of adding 4.328, 13, and 5.45?
-The final rounded result is 23, rounded to the least number of digits to the right of the decimal point in the original numbers.
Outlines
📚 Understanding Significant Figures
This paragraph introduces the concept of significant figures and how to determine their count in various numbers. It explains that every non-zero digit is significant and zeros between non-zero digits are also significant. The paragraph clarifies the significance of trailing zeros in the presence or absence of a decimal point and provides examples to illustrate the rules. Additionally, it discusses the irrelevance of leading zeros in determining significant figures and poses a quiz for viewers to apply these concepts to different numbers.
🔢 Counting Significant Figures in Numbers
The second paragraph continues the discussion on significant figures by analyzing specific numbers to determine their significant figures. It addresses the significance of trailing zeros in the presence of a decimal point and zeros between non-zero digits. The paragraph also explains the process of counting significant figures in numbers with leading zeros and provides a step-by-step analysis of example numbers, including those with decimal points and trailing zeros.
⚖️ Rounding Numbers in Multiplication and Division
This paragraph focuses on the process of rounding numbers when performing multiplication and division, emphasizing the importance of maintaining the correct number of significant figures. It demonstrates how to round the result of a multiplication to the least number of significant figures present in the original numbers. The paragraph provides examples, including the multiplication of 4.6 by 3.52 and the division of 96.752 by 3.541, showing the calculation process and the decision-making involved in rounding to the appropriate number of significant figures.
📉 Rounding in Addition and Subtraction
The final paragraph discusses rounding in the context of addition and subtraction, particularly addition. It explains the method of aligning numbers by their decimal points and rounding the final answer to the least number of digits to the right of the decimal point in the original numbers. The paragraph provides examples, such as adding 2.36 and 12.1, and demonstrates how to determine whether to round up or down based on the digit following the last significant figure. It concludes with a brief mention of additional resources for viewers interested in further exploring the topic of significant figures.
Mindmap
Keywords
💡Significant Figures
💡Non-zero Numbers
💡Zeros
💡Decimal Point
💡Trailing Zeros
💡Leading Zeros
💡Rounding
💡Multiplication and Division
💡Addition
💡Quiz
Highlights
The video provides a quick review of significant figures and how to determine them in numbers.
Every non-zero digit is a significant figure, as demonstrated with the number 846 having three significant figures.
Zeros between non-zero digits are significant, making 704 have three significant figures.
Trailing zeros to the right of a non-zero number are significant if there is a decimal point, as in 500.0 having four significant figures.
Leading zeros are never significant, as shown with 0.075 having only two significant figures.
The video offers a quiz to determine the number of significant figures in various numbers, such as 42.50 and 7080.
The importance of rounding numbers when multiplying or dividing to maintain the correct number of significant figures is discussed.
An example is given on how to round the result of multiplying 4.6 by 3.52 to two significant figures, resulting in 16.
The video explains that when multiplying or dividing, the final answer should be rounded to the least number of significant figures in the original numbers.
Additional examples of multiplication and division are provided to illustrate the rounding process.
The video covers the process of rounding numbers in addition and subtraction, emphasizing the least number of digits to the right of the decimal point.
An example of adding 2.36 and 12.1 is given, showing how to round the result to one decimal place to get 14.5.
The concept of significant figures is applied to more complex addition problems, such as adding 4.328, 13, and 5.45.
The final answer of the addition problem is rounded to 23, demonstrating the rounding process in action.
The video encourages viewers to check out another video for more in-depth information on significant figures.
A link to the more detailed video on significant figures is promised in the description for those interested in further learning.
The video concludes with a reminder to subscribe to the channel and turn on notifications for updates on new videos.
Transcripts
this video is going to be a quick review
of significant figures
the first thing that you need to be able
to do
is determine how many significant
figures are in a number
so for example let's say if we have the
number 846
how many significant figures are there
every non-zero number
is a significant figure so there's three
significant figures in this number
another example 3546
has four significant figures
now let's say if we have a zero
in between two non-zero numbers
is that zero significant
all zeros between two non-zero numbers
will be significant so
704 has three significant figures
5006
has four significant figures
now what about zeros
to the right of a non-zero number like
500
how many significant figures are there
in this
number it all depends on if there's a
decimal point or not
if we do not have a decimal point the
zeros to the right which are called
trailing zeros are not significant
so this would be only one significant
figure
in this case the trail and zeros are
significant so this would be three
significant figures
likewise if we had 500.0
this would be four significant figures
now what about the zeros to
the left of a number
like this point zero seven five
are these zeros the leading zeros are
they significant
leading zeros are never significant
so there's only two significant figures
the seven and the five
so let's say if we had point zero zero
eight three six
only these three numbers will be
significant
so to review let's try this example
.0050830
how many significant figures are in this
number
so looking at the leading zeros
remember the leading zeros
are not significant
the zeros that are in between
two nonzero numbers
those are significant
and the trailing zeros
are only significant
if
there is a decimal point which we do
have
therefore
these five digits are significant
so we're gonna have five significant
figures
so what i'm gonna do at this point is
give you a quiz
and i want you to determine how many
significant figures are in the following
numbers
so the first one is going to be 42.50
and the second one is 7080
and then
thousand
fifty with a decimal point
and then point zero zero seven zero
three
next we have point
zero eight zero six zero
and then 5030.0
and finally 750.064080
go ahead and determine the number of
significant figures
in each of those numbers
by the way for those of you who want
harder examples or maybe just more
examples
i have another video on youtube
that is about an hour and a half long
but it really goes deep into this topic
so for those of you who want to master
the concept of sig figs you can check
out uh that video i'm gonna post the
link in the description section of this
video so feel free to take a look at
that when you get a chance
also if you're going to subscribe to
this channel
make sure to click the notification bell
if you want to receive any updates
of any new videos that i'm going to post
in the future
so let's go ahead and begin
so four thousand two hundred fifty how
many significant figures does it have
so the zero at the right do we count it
well it's a trailing zero and there is
no decimal point so we're not going to
count it
so therefore we can only count these
three nonzero numbers
so we have three significant figures in
the first example
now what about the second example
how many significant figures are there
well once again we don't have a decimal
point
so we cannot count that zero
but what about the zeros in between
nonzero numbers
so those zeros we can count so therefore
this answer i mean this problem also
have a
three significant figures
now for the next one
there is a decimal point
so the trailing zero is counted
and all of the zeros in between the 3
and 5 are also counted
so this example is going to have 5
significant figures
for the next one we do have a decimal
point but there are no trail and zeros
we do have some leading zeros but those
will not be counted
so only these three digits will be
counted
so there's three significant figures in
that number
for the next one
we do have
a trail in zero which will be counted
the leading zeros will not be counted
so there's only four
significant figures
now in the next number 5030
we have a decimal point
so all of the trailing zeros
will be counted
and
the zero between the three and five
that's always counted so we have a total
of five significant figures
for the last example
all of the zeros in between the non-zero
numbers are counted and since we have a
decimal point the zero to the right is
also counted so everything is counted in
this example
so there's let's see one two three four
five six seven eight nine so we have
nine significant figures
for that problem
now the next thing that you need to be
able to do
is
you need to be able to round
a number when multiplying or dividing so
for instance let's say if we're
multiplying 4.6
by
3.52
how can we round our answer
with the appropriate number of
significant figures
well the first thing we need to do is
perform the calculation
so 4.6 times 3.52
if you type that into your scientific
device
your calculator will give you 16.192
now how should we round this answer to
the appropriate number of significant
figures
what would you say
what we need to do first is we need to
determine
the least number of significant figures
in the first two numbers that we've
multiplied already
so in the first number 4.6
there's two significant figures
in the second number 3.52
there's three significant figures so
when you're multiplying or dividing you
need to round your final answer
to the least number of significant
figures
in
the original numbers that you used to
multiply to get your final answer so
basically we need to round this answer
to two sig figs
so
writing it from left to right we have
the first digit which is a one and then
the second one is a six
now already this is two significant
figures
so the last number that we need to look
at is the six
should we keep it at six
or should we round it up to seven
and so we need to look at the next
number
if it's five or more then we need to
round the six to a seven if it's four or
less then we're gonna round down we're
gonna keep the six
and because it's
four or less it's one we're going to
round down
so our answer is 16
rounded to the appropriate number of sig
figs
now let's work on some other examples
let's multiply 5.64
by three point
or rather let's choose a higher number
by twelve point four
five eight
and let's divide
ninety six point seven five two
by three point
go ahead and try those two examples
round your answer to the appropriate
number of significant figures
so first let's type this in
the calculator
so 5.64 times 12.458
so the calculator gives us
70.26312
now the first number has three
significant figures and the second
number has five significant figures
so we have to round our answer to the
least number of significant figures
so that's three
so how can we round
seventy point two
six three one two
to three significant figures
so we're gonna need the first number
the second one
and the third one
should we keep it a two or should we
round it up to a three
looking at the next number
to the right of the two
it definitely falls in the category of
five or more so that tells us that we
need to round up we need to round the
two to a three
so the answer for this example is 70.3
and it has three significant figures
this answer has a total of seven
significant figures
now let's try the next example
so let's begin by dividing
96.752
by three point five four one
and so you should get twenty seven
point three two
three three
five
four nine eight
now the first number has
five significant figures
and the second number has four
so like always when multiplying or
dividing you need to round your final
answer
to the least number of significant
figures in this case four
so looking at the fourth digit
or the fourth significant figure
starting from the left
should we keep it at a two or should we
round it up to a three
so looking at the next number it falls
in the category of four or less
so we're going to keep the two
so our final answer is 27.32
now let's talk about addition and
subtraction but mostly addition
so let's say if we wish to add 2.36
plus
12.1 how can we round our answer to the
appropriate number of significant
figures
so if we add these two numbers
this will give us 14.46
but what should we do here
for this type of problem it's better
to
write the problem like this
now you need to round your final answer
to the least number of digits
to the right of the decimal point
so what i like to do is draw a line
because for 12.1 there is no number
to the right of the one
and so we're not going to have any
number to the right of this line
but now if we add the two numbers it's
going to give us 14.46
so what we're going to do is
we're going to keep
this significant figure but we need to
determine if it should stay a 4 or if we
should round it up to a 5.
looking at this number
it's
greater than 5 so we need to round this
number up
so our answer is going to be 14.5
and that's how you supposed to do it
when adding or subtracting
let's try another example 4.328
plus 13
plus 5.45
so go ahead and try that problem
well first we need to add
so we have an eight two plus five is
seven three plus four is seven
and then
four plus three plus five is twelve
carry over the one
and one plus one is two so we get twenty
two point
eight
now what should we do next
how can we round it
so what we need to do now is determine
which number
has the least number of digits to the
right of the decimal point
and so that's the second number
so we're going to draw the line here
because it has nothing on the right side
of that line
so therefore our final answer should
only contain
these two digits
but we're going to use the 7
to determine what we need to do to the
2. should we keep it a 2 or round it up
to a 3
well seven is more than five so we're
going to round the two up to a three
so our answer is going to be 23
and that's basically it for this video
so once again if you want more problems
on significant figures
check the link in the description
section of this video
for
the other video where
it's it goes into more detail on this
topic thanks again for watching
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