Transcript Significant figures Some numbers matter more than others…

Significant figures
Some numbers matter more than
others…
Measurements…
• In some measurements, the zeros are just
place holders…
• Example:
– There are 1400 students at LHS.
– This doesn’t mean 1400 exactly. Just close.
– Those zeros at the end don’t matter very
much, because they aren’t accurate.
Significant Figures
• Numbers that are really measured are
called significant figures, or sig figs.
• How do we tell which numbers are sig
figs?
• Arrow trick!
If there is a decimal…
• If there is a decimal, we bring an arrow from the
left…
.0004560
• The arrow goes through any zeros.
• It stops when it hits a number.
• Everything left is a sig fig…
Which digits are sig figs?
.000005438
.02020
.00438
1.0008
If there is no decimal…
• If there is no decimal, we bring an arrow from
the right…
780000
• The arrow goes through any zeros.
• It stops when it hits a number.
• Everything left is a sig fig…
Which digits are sig figs?
354 000
36 540
23 500 000
100 000
Now let’s mix them up!
• You have to decide whether the arrow will
come from the left or the right…
546500
.00254
1.000
Why does this stuff matter?
• One of our goals is to make
measurements that are both accurate and
precise.
• What’s the difference?
– Accuracy is whether or not you hit the target
– Precise is whether or not you get the same
results each time
Demonstration!
Multiplying…
• Today, we will multiply some sig figs…
• The secret is to make sure that your
answer has the same number of sig figs
as your measurement.
Example
• 5.436 x 1500 = 8154
• But since 1500 only has 2 sig figs, we
round to 8200
Another
• 7.15 x 12.00 = 85.8
• This one is fine as it is, because 7.15 only
has 3 sig figs. Our answer needs 3 sig
figs.
• If we wrote 85.80 it would be too many.
Who cares?
• Scientists…
• If I take a good measurement (17.000) and I
multiply it by something that is not as accurate
(like 30), my answer shouldn’t be all that
accurate.
• It’s like counting exactly how many jelly beans
you have, and then just guessing how many to
give to your friend. Why did you count exactly if
you weren’t going to divide exactly?
Today’s activity
• We are going to try to be precise and
accurate in today’s activity.
• To help prepare you, we need to review
some geometry terms…
For a block…
• Perimeter is each
edge length added
together…
4xL
4xW
+4xH
L
W
L
W
H
H
H
W
L
H
W
L
Area of a face
• There are three
different faces to each
block:
• Bottom (top)
H
LxW
• Side
WxH
• Front (back)
LxH
W
L
Also for a block…
• Volume
LxWxH
H
W
L
Also remember…
• You will have two digits to the right of the
decimal for every measurement today.
• You will need your own sheet of paper.