Significant figures

1
Significant figures

• Some numbers matter more than others

2
Measurements

• In some measurements, the zeros are just place
  holders
• Example
• There are 1400 students at LHS.
• This doesnt mean 1400 exactly. Just close.
• Those zeros at the end dont matter very much,
  because they arent accurate.

3
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!

4
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

5
Which digits are sig figs?

• .000005438
• .02020
• .00438
• 1.0008

6
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

7
Which digits are sig figs?

• 354 000
• 36 540
• 23 500 000
• 100 000

8
Now lets mix them up!

• You have to decide whether the arrow will come
  from the left or the right
• 546500
• .00254
• 1.000

9
Why does this stuff matter?

• One of our goals is to make measurements that are
  both accurate and precise.
• Whats the difference?
• Accuracy is whether or not you hit the target
• Precise is whether or not you get the same
  results each time

10
Demonstration!
11
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.

12
Example

• 5.436 x 1500 8154
• But since 1500 only has 2 sig figs, we round to
  8200

13
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.

14
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 shouldnt be all that
  accurate.
• Its 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
  werent going to divide exactly?

15
Todays activity

• We are going to try to be precise and accurate in
  todays activity.
• To help prepare you, we need to review some
  geometry terms

16
For a block

• Perimeter is each edge length added together
• 4 x L
• 4 x W
• 4 x H

L
W
W
L
H
H
L
H
H
W
W
L
17
Area of a face

• There are three different faces to each block
• Bottom (top)
• L x W
• Side
• W x H
• Front (back)
• L x H

H
W
L
18
Also for a block

• Volume
• L x W x H

H
W
L
19
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.