Tip:
Highlight text to annotate it
X
Bo: Hey guys.
Billy: Hey, Bo.
Bobby: Hi, Bo.
Singing Voiceover: Flipping Physics
Mr. P.: Ladies and gentle people,
the bell has rung, therefore class has begun,
therefore you should be seated in your seat,
and ready and excited to learn
about significant figures.
So, let me hear you get excited.
Billy: Yay!
Bo: [sarcastically] Wooooo.
Mr. P.: Significant figures are a necessary part
of any math-based science.
We are going to be manipulating data,
and we need to know how to do that.
The basic concept is
that significant figures are the digits
in your number that were actually measured
plus one estimated digit.
For example, we can measure the length
of this dry erase marker to
120 milimeters.
But we can actually estimate one beyond that
to get 120 milometers plus 1/10th of a millimeter
to get 120.1 milimeters.
The key here though is
to know how many significant digits you have
that comprise your significant figures.
Here are the basic rules,
and please understand
that no two different science books have the exact same rules,
but they all amount to the exact same thing.
So they all come up with the same result.
So here are my rules of significant figures.
Number 1.
(writing on a white board)
Mr. P.: All nonzero digits are significant.
Second rule.
(writing on a white board)
Mr. P.: Zeros between other nonzero digits are significant.
Therefore, Billy, how many digits
in the number 70.2 are significant?
Billy: Three.
The 7 and the 2 are significant
because they are nonzero,
and the 0 is significant
because it is between two other nonzero digits.
Mr. P.: Correct.
There are three sig figs in 70.2.
Let's write down the next rule.
(writing on a white board)
Rule number three: Zeros that are to the left
of nonzero digits are not significant.
Therefore, Bobby, how many digits
in the number 0.045 are significant?
Bobby: Two.
The 4 and 5 are significant
because they are nonzero
and both zeros are not significant
because they are to the left of the 4 and 5.
Bo: Hold up.
In the 70.2 isn't the 0 to the left
of 2 and therefore not significant?
Mr. P.: Good question, Bo.
Please realize that the second rule trumps the third.
Therefore, the 0 in 70.2 is significant because it is
between two nonzero numbers.
All right, let's write down rule number four.
(writing on white board)
Rule number four: Zeros at the end
of a number are significant only
if they are to the right of a decimal point.
Therefore, Bo, how many significant figures
on the number 70.0?
Bo: Three.
All the zeros are significant
because there is a number on the right
of the decimal.
Mr. P.: Great.
Now I'm going to put numbers on the board
and call on individuals to tell me
how many significant figures are in each number.
If you do not understand an answer,
it is your responsibility to ask.
(writing on white board)
Billy, 4.7.
Billy: Two.
Mr. P.: Bo, 100.
Bo: One.
Mr. P.: Bobby, 706.
Bobby: Three.
Mr. P.: Bo, 400.0.
Bo: Four
Mr. P.: Billy, 0.002.
Billy: Four.
Mr. P.: Bobby, 0.0020.
Bobby: Um, five?
Mr. P.: Remember, it is your responsibility to ask.
I won't always let you know when something is wrong.
It's important that we recognize our mistakes
so that we can learn from our mistakes.
Billy: All the zeros are not significant in 0.002
because they are to the left of an integer
and not between nonzero numbers.
So there is only one sig fig in 0.002.
Bobby: Right.
And the only zero that is significant
in 0.0020 is the zero on the far right
because it is to the right of a nonzero number.
Mr. P.: Great.
Let's try a couple more.
(writing on white board) Bo, how about 0.0002047?
Bo: Four.
Mr. P.: Bobby, 1.0?
Bobby: Two.
Mr. P.: Billy, 104,020?
Billy: Five.
Mr. P.: All right, please realize that
if you understand all of those examples
then you understand all
of the significant figures rules.
Congrats.
Now, let's work actually the other way.
Bo, how would you illustrate the number 1200
with three sig figs?
Bo: You'd just put a decimal after the last zero.
Bobby: Wouldn't that be four significant figures?
Bo: Oh yeah, that's four.
Billy: We would have to use scientific notation,
so it would need to be 1.20 x 10^3, right?
(writing on white board)
Mr. P.: Yes.
1.20 has three significant digits
and multiplying by 10^3, or 1000,
makes it 1200.
We're going to end up using a lot
of scientific notation in this class.
So, Bobby, how would we write 0.002
with three significant figures
and in scientific notation?
Bobby: That would be 2.00 X 10^-4.
To the -4 because we need
to move the decimal four places to the left
to go from 2.00 x 10^-4
to 0.0002.
Billy: Couldn't you just write 0.00200?
Mr. P.: Absolutely, Billy.
However, that isn't quite what I asked for.
I asked for it not only with three significant digits
but also to show it in scientific notation.
Billy: Oh, yeah.
Mr. P.: That's my introduction
to significant figures.
I hope you enjoyed learning with me today.
I enjoyed learning with you.
Voiceover: Lecture notes are available
at FlippingPhysics.com
Please enjoy lecture notes responsibly.
Man swinging: Ahhh!
(running)
Man swinging: Ahh!