measured & counted numbers when you use a measuring tool to determine a quantity such as your...
TRANSCRIPT
Measured & counted numbers• When you use a measuring tool to
determine a quantity such as your height or weight, the numbers you obtain are called measured numbers.
Counted numbersObtained when you count objects• 2 soccer balls• 1 watch• 4 pizzasObtained from a defined relationship• 1 foot = 12 inches• 1 meters = 100 cm
Not obtained with measuring tools
Measurements:Accurate or Precise?
Creating definitions and clarifying terms
Precision• Precision is the ability to _______________and
come up with the same value every time.• It is an indication of __________a series of
measurements are to each other.• In general, the more decimal places you have,
the more precise your measurement is.
Precision• The idea of precision is very closely aligned
with the idea of significant figures.• A large number of significant figures
suggests a high degree of precision.• In our next class we will learn all about sig
figs. Now, relax
Which is the most precise balance?
Accuracy• An indication of how
________________________ (often theoretical)
The closer you are to the real, accepted value, the more accurate you are.
Accurate or Precise?Case 1
• In the diagram, what can we say about the group of arrows in terms of
accuracy:
precision:
Accurate or Precise?Case 1
• In the diagram, what can we say about the group of arrows in terms of
accuracy:low (as a group)
precision:low
Accurate or Precise?Case 2
• In the diagram, what can we say about the group of arrows in terms of
accuracy:
precision:
Accurate or Precise?Case 2
• In the diagram, what can we say about the group of arrows in terms of
accuracy:low
precision:high
Accurate or Precise?Case 3
• In the diagram, what can we say about the group of arrows in terms of
accuracy:
precision:
Accurate or Precise?Case 3
• In the diagram, what can we say about the group of arrows in terms of
accuracy:high
precision:high
Can we ever be 100% certain??Nope!This is what we call ‘uncertainty’ in measurements.
Experimental uncertainty
• It is the estimated amount by which a measurement might be in error
• Usually expressed as +/-• The smaller the uncertainty, the more the
precision…
Experimental uncertainty
Assume you measured a temperature to be 37.5 C°What would the uncertainty be?Uncertainty is always in the last digit!What does this mean?
Experimental uncertainty
This means, the actual degree is somewherebetween
How to read a measurement scale
Taking measurements
Example b) page 31
Volume readings
Graduated cylinder readings
Time to practice!
Hebden page29 #44 page32 #48(A,C,E) page34 #50(A,D,G) page35 #51(A,C) and #52(A,B)
I am here to help
Measurements • Why do we care??????
• Measured quantities have uncertainties in them. It is impossible to find the EXACT value…so what do we use?
Significant figures• They are measured or meaningful digits.How do we know if a number is a ‘sig fig’ or
not? • Let us proceed, shall we?
Two major cases to know
#1: When there are no decimal points
#2: When there are decimal points
#1: when there are no decimal points
• Count every single number you see as a significant figure, EXCEPT for ZERO.
• BUT…..Zeroes in between two non-zero digits are significant. All other zeroes are insignificant.
#1: when there are no decimal points
• How many sig figs do the following numbers have??
345, 5557, 300, 4120, 4005, 40050
#2: when there are decimal points
• Start from the left side of the number, ignore all the zero's on the left side of the decimal points ( aka leading zero's). Only start counting at the first non zero digit. Once you start counting, continue until you run out of digits.
#2: when there are decimal points
• Example: how many sig figs do the following numbers have?
32.670, 0.0001, 0.034780, 44.4, 00.9090
Significant figures
“sig figs”
0.5200.00255000.02300120035500.2.0 x 105
3214632 do not expand
Significant figures
“sig figs”2.50020.0065050010.02003000.02010200200.2.0 x 102
2. x 102
534641321
Adding and Subtraction with Significant Figures
When adding or subtracting sig figs, only round off the final answer ( never when still calculating) to the LEAST NUMBER of decimal places contained in the calculations. 1.
21.036 + 22.1
Adding and Subtraction with Significant Figures
When adding or subtracting sig figs, only round off the final answer ( never when still calculating) to the LEAST NUMBER of decimal places contained in the calculations
3.301.2256
- 0.36
Adding and Subtraction with Significant Figures
4. 8.053 x 104
+ 2.3 x 104
Adding and Subtraction with Significant Figures
5.2.463 x 105
+ 5.006 x 102
Adding and Subtraction with Significant Figures
6. 5.331 x 10-4
- 2.126 x 10-5
When changing exponents, remember…..if you change the lower exponent to the higher exponent. You are making the exponent larger so make the number smaller. It is a trade !
HOMEWORK• PAGE 40 #57 (A,B,C,E,F,I,J)