- Hey, guys.
- Hey, Bo.
- Hi, Bo
♫ Flipping Physics ♫
- Ladies and gentlepeople,
the bell has rung, therefore class has begun,
therefore you should be seated in your seat ready
and excited to learn about significant figures.
So, let me hear you get excited.
- Oh boy!
- Yipee!
- Significant figures are a necessary part
of any math-based science.
We are going to be manipulating data
and we need to know how significant figures work.
The basic idea with significant figures is
they 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 132 millimeters,
and we can actually estimate that the measurement is
one-tenth of a millimeter less than 132,
or 131.9 millimeters.
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 I have yet to find any two science textbooks
that have the exact same rules of significant figures.
However, they all amount to the same thing.
So, here are my rules of significant figures.
Rule number one, all nonzero digits are significant.
Rule number two, zeros between significant digits
are significant.
Therefore, Billy, how many digits
in the number 70.2 are significant?
- Three.
The seven and the two are significant
because they are nonzero,
and the zero is significant because it is
between two other significant digits.
- Correct. There are three significant figures in 70.2.
Rule number three, zeros to the left
of nonzero digits are not significant.
Therefore, Bobby, how many digits
in the number 0.045 are significant?
- Two.
The four and five are significant
because they are nonzero,
and both zeros are not significant
because they are to the left of the four and five.
- Hold up.
In the 70.2, isn't the zero to the left of the two
and, therefore, not significant?
- That is a good question, Bo,
and it turns out that the second rule trumps the third rule.
Therefore the zero in 70.2 is significant
because it is between two significant digits.
Zeroes at the end of a number are only significant
if they are to the right of the decimal point.
Therefore, Bo, how many significant figures
in the number 70.0?
- Three.
The zero to the right of the decimal is significant
because it is at the end of the number,
and to the right of the decimal.
And the zero to the left of the decimal is significant
because it is between two significant digits.
- 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.
And if you do not understand an answer,
it is your responsibility to ask.
Billy, 4.7?
- Two.
- Bo, 100?
- One.
- Bobby, 706?
- Three.
- Bo, 400.0?
- Four.
- Billy, 0.002?
- Four.
- Bobby, 0.0020?
- Uh, five?
- Remember, it is your responsibility to ask
when you do not understand something.
I won't always correct mistakes as we make them
because it is important that we make mistakes
so that we can recognize our mistakes
so that we can learn from our mistakes.
- All the zeroes are not significant
in 0.002 because they are to the left
of a nonzero number and not between significant digits.
So, there's only one sig fig in 0.002.
- 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.
- Great.
Bo, how about 0.002047?
- Four.
- Bobby, 1.0?
- Two.
- Billy, 104,020?
- Five.
- All right.
Please realize that if you understand all of these examples
then you understand all of the rules
of significant figures.
Congratulations!
Now, let's work the other direction.
Bo, how would you illustrate the number
1,200 with three significant figures?
- Just put a decimal after the last zero.
- Wouldn't that be four significant figures?
- Oh yeah, that's four.
- We would have to use scientific notation.
So, it would need to be 1.20
times ten to the third power, right?
- Yes, 1.20 has three significant figures,
and multiplying by ten to the third power,
or 1,000, makes it 1,200.
Bobby, how would we write 0.002
with three significant figures
and in scientific notation?
- That would be
2.00 times ten to the negative three.
2.00 for three sig figs
and times ten to the negative three
because we need to move the decimal three places
to the left.
- Couldn't you just write 0.00200?
- Absolutely Billy.
0.00200 does have three significant figures.
However, I asked for it also in scientific notation.
- Okay, thanks.
- That is my introduction to significant figures.
Thank you very much for learning with me today.
I enjoyed learning with you.