Significant Figures - A Fast Review!

Summary

This 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

00:00

📚 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.

05:00

🔢 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.

10:00

⚖️ 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.

15:01

📉 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.

Keywords

💡Significant Figures

Significant figures are the digits in a number that carry meaningful information about its precision. In the video, the concept is central to understanding how to accurately represent the precision of measurements and calculations. For example, the number 846 has three significant figures, indicating that the measurement is precise to the hundreds place.

💡Non-zero Numbers

In the context of significant figures, non-zero numbers refer to any digit other than zero that contributes to the count of significant figures. The video explains that every non-zero digit is inherently significant, as seen when counting the significant figures in the number 3546, which has four significant figures.

💡Zeros

Zeros play a specific role in determining significant figures. The video clarifies that zeros between non-zero digits are significant, as in the number 704, which has three significant figures, including the zero between the seven and four. However, leading zeros, those to the left of the first non-zero digit, are not significant.

💡Decimal Point

The presence of a decimal point affects the significance of trailing zeros in a number. The video illustrates that if there is a decimal point, as in 0.075, the trailing zeros are significant, contributing to the total count of significant figures, which in this case is two.

💡Trailing Zeros

Trailing zeros are zeros that appear to the right of the last non-zero digit in a number. The video explains that their significance depends on the presence of a decimal point. Without a decimal point, as in 500, the trailing zeros are not significant, but with a decimal point, as in 500.0, they are significant.

💡Leading Zeros

Leading zeros are zeros that appear to the left of the first non-zero digit in a number. The video emphasizes that these zeros are never considered significant figures, as in the number 0.0075, where the leading zeros before the seven are not counted towards the significant figures.

💡Rounding

Rounding is the process of adjusting a number to a certain level of precision, typically to the nearest significant figure. The video demonstrates rounding through examples of multiplication and division, where the final answer is rounded to the least number of significant figures present in the original numbers involved in the operation.

💡Multiplication and Division

These operations are highlighted in the video as scenarios where the number of significant figures in the result must be determined. The video explains that when multiplying or dividing, the result should be rounded to the least number of significant figures of the numbers involved. For instance, multiplying 4.6 (two significant figures) by 3.52 (three significant figures) results in a number that should be rounded to two significant figures.

💡Addition

While the video focuses more on multiplication and division, it also touches on addition and how to round the result to the appropriate number of significant figures. The video uses the example of adding 2.36 and 12.1, emphasizing that the final answer should be rounded to the least number of digits to the right of the decimal point in the numbers being added.

💡Quiz

The video includes a quiz as an interactive way for viewers to apply their understanding of significant figures. The quiz challenges viewers to determine the number of significant figures in various numbers, reinforcing the concepts taught in the video and providing practical examples such as the number 42.50, which has three significant figures.

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