Transcript Precision - Uplift Education

Measurement: Accuracy,
Precision, & Error
August 6 & 7, 2015
How well can I measure
this object?
Accuracy vs Precision
Accuracy
the extent to which a reported measurement
approaches the true value of the quantity measured –
how close is the measurement to the reality.
Precision
the degree of exactness of a measurement (results
from limitations of measuring device used).
Accuracy vs. Precision
Example: game of darts
precise, not
accurate
accurate,
not precise
neither
accurate nor
precise
A
B
C
accurate
and precise
Which ruler will allow the most
precise measurements? Why?
Accuracy vs. Precision
Example: game of darts
precise, not
accurate
accurate,
not precise
neither
accurate nor
precise
A
B
C
accurate
and precise
Which ruler will allow the most
accurate measurements? Why?
Is the most precise instrument
always the most accurate
instrument? Why or why not?
Accuracy vs. Precision
Another
example:
Discuss in
pairs
Errors in Measurement
Random Errors
Measured value can be above OR below
the true value with equal probability.
Example: normal user error
Systematic Errors
• Due to the system or apparatus
• Errors are consistently in one direction
(always high or always low)
Examples:
– Apparatus calibrated incorrectly
– Scale not zeroed
– User making the same error
Errors in Measurement
Turn & Talk with table partner
Younger partner …
Which type of error would be more common when using
a ruler?
Describe an example of each type of error with a ruler.
Older partner –
Which type of error would be more common when using
a digital scale?
Describe an example of each type of error with a digital
scale.
Together –
Does taking more measurements reduce each type of
error? Why or why not?
Significant Figures
Can measurements ever be exact? No!
Significant figures =
reliably known measurements + one estimate
52 mL – reliably known
0.8 – estimate
Measurement = 52.8 mL
How many significant figures? 3
What is the precision of the
measurement?
+ 0.2
mL
Significant Figures
In table groups …
What are the known measurements? 2.3 cm
What is estimated? 0.04 cm
What is overall measurement? 2.34 cm
How many sig figs? 3
Significant Figures
Which numbers in a measurement are significant?
The simple answer:
all measured & estimated digits are significant
all ‘place holders’ are not
Significant Figures
Which numbers in a measurement are significant?
• All non-zero numbers are significant
Significant Figures
Which numbers in a measurement are significant?
• All non-zero numbers are significant
• All zeros between other non-zero digits are
significant. (e.g. 503 km)
Significant Figures
Which numbers in a measurement are significant?
• All non-zero numbers are significant
• All zeros between other non-zero digits are
significant. (e.g. 503 km)
• Zeros to the left of non-zero digits are not significant
(e.g 0.0087 L)
Significant Figures
Which numbers in a measurement are significant?
• All non-zero numbers are significant
• All zeros between other non-zero digits are
significant. (e.g. 503 km)
• Zeros to the left of non-zero digits are not significant
(e.g 0.0087 L)
• Zeros to the right of a decimal are significant. (e.g.
23.50 g)
Significant Figures
Which numbers in a measurement are significant?
• All non-zero numbers are significant
• All zeros between other non-zero digits are
significant. (e.g. 503 km)
• Zeros to the left of non-zero digits are not significant
(e.g 0.0087 L)
• Zeros to the right of a decimal are significant. (e.g.
23.50 g)
• Zeros to the right of a non-decimal are ambiguous.
Without other info, assume not significant. (e.g. 5200
m)
Significant Figures
How can you make it obvious whether zeros at the end
are significant or not?
Use scientific notation!
3000 km
3.0 X 103 km
Sig figs are ambiguous. 1, 2, 3, or 4?
Sig figs = 2
Alternatively, you can put a line over / under the last
significant digit (e.g. 3000 km)
Significant Figures
How many significant figures?
4509.0 g
0.0087 kg
0.0908 mm
13000 mL
Significant Figures
How many significant figures?
4509.0 g
5 sig figs
0.0087 kg
2 sig figs
0.0908 mm
3 sig figs
13000 mL
2 sig figs
Significant Figures
Individually, identify the number of significant figures
5000.0 g
3008 L
0.0090 m
5080 cm
Significant Figures
Individually, identify the number of significant figures
5000.0 g
5 sig figs
3008 L
4 sig figs
0.0090 m
2 sig figs
5080 cm
ambiguous – without further info, assume
3 sig figs
Calculations with Sig Figs
When making calculations with measurements, the
least precise measurement determines the precision of
the final answer.
Calculations with Sig Figs
When making calculations with measurements, the
least precise measurement determines the precision of
the final answer.
Example:
If a 5.6 meter flag is placed
on top of a 3000 m
mountain, how high is the
of the flag?
Calculations with Sig Figs
When making calculations with measurements, the
least precise measurement determines the precision of
the final answer.
Example:
If a 5.6 meter flag is placed
on top of a 3000 m
mountain, how high is the
of the flag?
IT DOESN’T MAKE SENSE TO
SAY 3005.6 m.
Calculations with Sig Figs
When adding or subtracting
The final answer has the same number of decimals as
the least precise measurement.
Example: 2.2 + 1.25 + 23.894 = 27.164 → 27.2
2.2??
1.25?
+23.894
27.164 → 27.2
You don’t know the second and third decimal
places in some measurements, so your answer
cannot reliably include those values.
Calculations with Sig Figs
When multiplying or dividing
The final answer has the same number of significant
figures as the least precise measurement.
Calculations with Sig Figs
When multiplying or dividing
The final answer has the same number of significant
figures as the least precise measurement.
Example: 121.30 x 5.35 = (648.955) = 649
(5 SF) x (3 SF) =
= (3SF)
Answer should be rounded up to 3 SF only
Calculations with Sig Figs
Do these individually.
4.3 km + 2.567 km + 6 km =
8.23 g – 1.04 g - 5.1 g =
45 mL X 5000 mL =
0.00085 mg ÷ 0.0090 mg =
Calculations with Sig Figs
Do these individually, then check with a table partner.
4.3 km + 2.567 km + 6 km = 13 km
8.23 g – 1.04 g - 5.1 g = 2.1 g
(1s digit)
(1 past decimal)
45 mL X 5000 mL = 200000 mL
(1 sig fig)
0.00085 mg ÷ 0.0090 mg = 0.094 mg
(2 sig figs)
Exit Ticket!
HW and HW Quiz
Closure
What were our objectives today,
and how well did we accomplish them?
How did we address our unit statement today?
What was our LP trait and how did we demonstrate it?