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2.2 notes.notebook
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August 24, 2016
2.2 Measurement UncertaintiesComparing Results:
disregard this section
degree of exactness of a measurement (like a tight groupingof arrows shot at a target) (getting basically the same results )
depends on instrument used (it's divisions)Generally, the precision is one half the smallest increment.
If an instrument (meterstick) measures to the nearest millimeter (mm) you would estimate and list the measurement to within at least 0.5 mm. An instrument like a micrometer can measure to 0.01 mm and you can estimate within at least 0.005 mm, therfore, it is more precise than the meterstick.
Accuracy and Precision
Accuracy and Precision
agreement of a measurement with a standard value (hitting the bullseye)
twopoint calibration: checks the accuracy of an insturment by 1) seeing if the instrument reads "0" when it should and 2) do it then also give the correct reading of an accepted standard.
Techniques of good measurement
avoid parallaxcontrol outside sources of error (heat, excess pressure)
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?
xxx
x
x xxx
x
x
x
x
xx xx
Significant Digits
Significant digits include all valid digits. This includes all digits up to the smallest increment of the instrument and then one estimated place further . You decide how many divisions you can estimate between the smallest increment.example: If you used a meterstick to measure the length of your book it would be about 0.2835 m (28.35 cm). The "3" digit in the smallest increment of the meterstick (the "mm") and the "5" represents the estimated value between the smallest increment. The estimated diget is valid so this measurement has 4 valid digits and therefore 4 sig. figs.
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Significant Digits
Significant digits include all valid digits. This includes all digits up to the smallest increment of the instrument and then one estimated place further. You decide how many divisions you can estimate between the smallest increment.
repeat
How you estimate is called Uncertainty of a Measurement and is indicated by a +/ following the listing of the measurement showing how many divisions you divided the smallest increment into. If you thought you could divide the millimeter increment into 10 estimated divisions you would list your textbook length measurement as 0.2835 ± .0001 m. The ± .0001 m states you divided the mm increment into 10 divisions are are confident the length is no smaller than 0.2834 m and no larger than 0.2836 m
Significant Digits
With digital instruments like this scale you can assume that all of the digits are significant and it can measure to the nearest pound and estimate to the nearest 0.1 of a pound.
http://www.eatsmartproducts.com/products
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Are all zeros significant?
1) All nonzero digits are significant
2) All final zeros after the decimal point are significant
3) Zeros between any two nozero digits are significant
4) Zeros used solely as placeholders are not significant
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Arithmetic with Significant DigitsWhen you use your measurements to calculate additionalcharacteristics/properties by adding, subtracting or multiplying/dividing you have to remember that your results can not be more precise than your measurements.
When you add/subtract in a calculation the place of significant digits in the measurements determines the place of significance in the answer.
1.2 mm+ 2.33 mm 3.53 mm = 3.5 mm
1.2 mm+ 2.33 mm 3.53 mm = 3.5 mm
the leftmost place of significance in the addends determine the rightmost place of significance in the answer
When you multiply/divide in a calculation the number of significant digits in the measurements determines the number of significant digits in the answer.
2.2 mx 1.24 m 2.728 m2 = 2.7m2
2 sig. figs.
3 sig. figs
answer has to have the least (2)
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Jon has 5 dimes. How many pennies is that?
1) write out the problem with the units you have on the left and the units you want on the right...(leave room for the conversion factor)
2) determine the conversion factor that is the identify of the two units (pennies/dimes) if you put a "1" in front of the largest unit (dimes), then the other unit (pennies) will always be larger than "1" (10 pennies/1dime)
units you have units you want
1)
2)
5 dimes ( ) = ___________ pennies
5 dimes ( ) = ___________ pennies10 pennies 1 dime
converting
Jon has 5 dimes. How many pennies is that? continued
3) arrange the units in the conversion factor so the units you have are on the bottom and the units you want are on the top
4) the units you have now cancel (dimes on top cancel with dimes on the bottom) and pennies remain
5) multiply the units you have by the conversion factor (5 x 10= 50..... 50 ÷ 1 = 50)
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23 cm = ______________ m
23 cm 1 m = .23 m 100 cm
23 x 1 = 23......... 23 ÷ 100 = .23........or 23 x 1 = .23 100
23 cm 1 m = .23 m 100 cm
units you want
units you have
cm x m = cm(m) .... cm(m) cm = m _..
review
1) have/want
2) conversion factor identity
3) range, "1" by biggest unit
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Mm = 106 m
pm = 1012 m
exponential separation
750 pm _______ Mm
7.5 x 102 pm = ______Mm 7.5 x 102 pm _100__Mm = _______Mm 10? pm( ( 6
12
7.5 x 102 pm _100__Mm = _7.5 x 10 16 Mm 10 18 pm( ( 6
1218
put a "1" (10 ) by the largest
prefix
0
=
0.12 km = ______ m
Another way to do the same conversion is to identify the exponent values of the measurement and the metric prefixes.
1) express the measured value in scientific notation
0.12 km = 1.2 x 10 1 km 2) insert your conversion factor with the proper metric units (what you have and what you need)
1.2 x 101 km ( ____m
____km
(
= ___________ m
3) put a "1" (or 100) by the largest prefix in the conversion factor
1.2 x 101 km ( ____m
____km
(
= ___________ m100
4) outside the conversion bracket list the exponent value of the metic prefix(s) inside the bracket. In this case "m" is a base unit with a value of 1, or 100 , hence the 0, and kilo means 1000, or 10 3, hence, the "3"
1.2 x 101 km ( ____m
____km
(
= ___________ m1000
3
5) list the exponential separation of the metric units in the conversion factor (in this case there an exponential separation of 3 (meaning 10 3 or 1000)
1.2 x 101 km ( ____m
____km
(
= ___________ m1000
33
6) This is now the value to insert in the conversion factor
( ____m
____km
(= ___________ m100
0
33
103
1.2 x 101 km
7) Because you listed your measurement in scientific notation you can list your primary units in your answer and then and then determine the exponent
( ____m
____km
(
= ___________ m100
103
1.2 x 101 km 1.2 x 10?
8) determine you exponent by add (because you're multiplying) and subtracting (because you're dividing)
( ____m
____km
(
= ___________ m = 1.2 x 102 m100
103
1.2 x 101 km 1.2 x 10?
101 x 103 is 1 + 3 which is 2 (10 2) 102 ÷ 100 is 2 0, which is 2
2 stands for 102 , that's the exponent in you answer
recap: 1 + 3 0 = 2
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mm = 103 m
pm = 1012 m
exponential separation
750 pm = _______ mm
7.5 x 102 pm = ______mm
7.5 x 102 pm 10 0 mm = _______mm 10 ??? pm( ( 3
12
7.5 x 102 pm _100__mm = _7.5 x 107_mm 109 pm( ( 3
12
2 + 0 = 2 2 9 = 7
add because you're multplyingsubtract because you're dividing
#1: rewrite in standard Scientific Notation#2 conversion factor with what you have on bottom and what you want on top#3 put a "1" (100) by the largest metric prefis you'll never have negative exponents
in the conversion factor!!! #4 find exponential separation of your metric prefixes#5 This separation is the exponent of your smaller prefix in the conversion factor#6 add subtract exponents!
conver
sion ste
ps
1100 ft/s = ________ m/s
1100 ft/s = _____ m/s(_____1 m3.28 ft
(
=
_
_335
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