Estimates,
Averages, and
Sig Figs
October 6, 2015
(2.2 in your books)
Meme Moment
Scientist of the Day
Jonas Salk
• Invented polio vaccine
• 58000 people used to get
polio in the US each year
o 1/3 of them ended up
partially paralyzed
o Iron lung
• Funded by March of
Dimes
• Refused to patent
invention
• Polio now gone in all but 3
countries
Percent Error
• Another way to evaluate accuracy is with percent error
(% err, % E, PE)
• In a good experiment, percent error is < 5%
𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 − 𝑡𝑟𝑢𝑒 𝑣𝑎𝑙𝑢𝑒
𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =
× 100%
𝑡𝑟𝑢𝑒 𝑣𝑎𝑙𝑢𝑒
• Sometimes you’ll see “theoretical” or “actual” instead of
“true” – this is still OK
• The top half of the equation is often an absolute value
I symbol |
Percent Error
• 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =
𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 −𝑡𝑟𝑢𝑒 𝑣𝑎𝑙𝑢𝑒
𝑡𝑟𝑢𝑒 𝑣𝑎𝑙𝑢𝑒
• 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =
10.75𝑔/𝑚𝐿−10.5𝑔/𝑚𝐿
10.5 𝑔/𝑚𝐿
• 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 =
0.25 𝑔/𝑚𝐿
10.5 𝑔/𝑚𝐿
× 100%
• 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 = 0.0238 × 100%
• 𝑃𝑒𝑟𝑐𝑒𝑛𝑡 𝐸𝑟𝑟𝑜𝑟 = 2.38%
× 100%
× 100%
8th grade
Range
Range: the spread of data
Math: biggest # - smallest #
In high school/college you might have a different
definition, but use this one for now.
Anomalous Data
• Sometimes you make a data set and one number
looks really weird
• This is anomalous data
• Anomalous data is useful – it can tell you if your
equipment isn’t working right, or maybe you forgot
to control for a variable
• If your averages and percent error are strange, look
for anomalous data
Significant Figures
• Significant figures = sig figs
• How scientists tell each other
how precise a number is.
• Sig figs are made up of all the
measured values (increments) +
one that we estimate
o Like how we measured volume in a
beaker, then estimated in between
the smallest marks
• From now on, all answers must be
in sig figs!
Sig the Fig
Zeroes in Sig Figs
•
•
•
•
A number that isn’t zero always counts
Zeroes in the middle always count
Zeroes at the start don’t count
Zeroes at the end don’t count unless there’s a decimal
Number
Significant Parts
# Sig Figs
45357
45357
5
405
405
3
200
200
1
200.00
200.00
5
200.5
200.5
4
0.0045
0.0045
2
10.
10.
2
More Sig Figs!
Number
Significant Parts
# Sig Figs
2502757
2502757
7
14.058000
14.058000
8
0.000450
0.000450
3
10000
10000
1
67
67
2
0100
0100
1
2.000
2.000
4
2.00200
2.00200
6
3850
3850
3
Adding/Subtracting Sig Figs
• Use the smallest number of decimal places (or tens,
hundreds, thousands, etc)
• Round to that number!
Multiplying/Dividing Sig
Figs
• Use the smallest number of sig figs
• Round to that number!
More Stuff
• If you are using a conversion factor like “1000 g/ 1 kg”
you have unlimited sig figs
• If you are using a counting number like “2 people,”
you have unlimited sig figs
Homework
• Worksheet! It’s double-sided and due Friday.
• All answers must be in sig figs.
• Worksheet covers 2.1 and 2.2.
Questions
• Any questions about the slides?
• Any new questions?