daily challenge 9/16
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Daily Challenge 9/16
• Is there a difference between accuracy and precision? Why or why not?
Accuracy vs. Precision
ACCURACY – HOW CLOSE A MEASUREMENT COMES TO THE TRUE VALUE; “CORRECT?”
PRECISION – HOW CLOSE A SERIES OF MEASUREMENTS ARE TO ONE ANOTHER; “Consistent?”
3.1
Accuracy vs. PrecisionACCURATE?
“CORRECT?”
PRECISE?
“REPEATABLE?”
NO NO
YES YES
NO YES
3.1
Determining Error
“KNOWLEDGE RESTS NOT UPON TRUTH ALONE, BUT UPON ERROR ALSO”
3.1
Determining Error
ERROR = EXPERIMENTAL VALUE – ACCEPTED VALUE
VALUE MEASURED IN
THE LAB
CORRECT VALUE
3.1
Determining Error
PERCENT ERROR =ERROR
× 100%ACCEPTED VALUE
ABSOLUTE VALUE!!
3.1
Determining Error
• Guess my weight…
• Observed?????
• Accepted/Correct Value- See drivers license
Determining Error
THE ACCEPTED VALUE FOR THE MELTING POINT OF SODIUM CHLORIDE IS 801°C. A STUDENT EXPERIMENTALLY DETERMINED THE MELTING POINT TO BE 702°C. DETERMINE THE ERROR AND THE PERCENT ERROR.
A
ERROR = EXPERIMENTAL VALUE – ACCEPTED VALUE
ERROR = 702°C 801°C
– 99°C
–
ERROR =3.1
1
Determining Error
THE ACCEPTED VALUE FOR THE MELTING POINT OF SODIUM CHLORIDE IS 801°C. A STUDENT EXPERIMENTALLY DETERMINED THE MELTING POINT TO BE 702°C. DETERMINE THE ERROR AND THE PERCENT ERROR.
A
PERCENT ERROR =ERROR
× 100%ACCEPTED VALUE
PERCENT ERROR =-99°C
×100% = 12%801°C
3.1
1
Significant Figures
• IN A MEASUREMENT, ALL OF THE DIGITS THAT ARE KNOWN, PLUS A LAST DIGIT THAT IS ESTIMATED.
• THE ESTIMATED DIGIT IS ALWAYS ONE PLACE HOLDER SMALLER THAN THE MARKED INTERVAL IN THE INSTRUMENT.
3.1
Measuring with Significant Figures
Determine the position of the marked (“smallest”) interval on the measuring device. What position can you read?
1
● 5 76 81 32 4
Tho
usan
ds
Hun
dred
s
Ten
s One
s
Ten
ths
Hun
dred
ths
Tho
usan
dths
Ten
Tho
usan
dths
Measuring with Significant Figures
Determine the estimated position . The estimated position is ALWAYS one position to the RIGHT of the marked interval.
For example: If the marked interval is the hundreds place, the estimated position is the tens place.
2
●1 32 4
Tho
usan
ds
Hun
dred
s
Ten
s One
s
Measuring with Significant Figures
Write the measurement to accurately reflect the marked interval, estimated position and unit.
3
3.4 m 3.4
Significant Figures
100 200 300 400 cm2
IN A MEASUREMENT, ALL OF THE DIGITS THAT ARE KNOWN, PLUS A LAST DIGIT THAT IS ESTIMATED.
MARKED POSITION: _____________________
ESTIMATED POSITION: _____________________
MEASUREMENT: _____________________
THE ESTIMATED DIGIT IS ALWAYS ONE PLACE HOLDER SMALLER THAN THE MARKED INTERVAL IN THE INSTRUMENT.
HUNDREDS
TENS
370 cm
3.1
Significant Figures
3
IN A MEASUREMENT, ALL OF THE DIGITS THAT ARE KNOWN, PLUS A LAST DIGIT THAT IS ESTIMATED.
MARKED POSITION: _____________________
ESTIMATED POSITION: _____________________
MEASUREMENT: _____________________
THE ESTIMATED DIGIT IS ALWAYS ONE PLACE HOLDER SMALLER THAN THE MARKED INTERVAL IN THE INSTRUMENT.
ONES
TENTHS
2.5 cm
1 2 3 4 cm
3.1
Significant Figures
4
IN A MEASUREMENT, ALL OF THE DIGITS THAT ARE KNOWN, PLUS A LAST DIGIT THAT IS ESTIMATED.
MARKED POSITION: _____________________
ESTIMATED POSITION: _____________________
MEASUREMENT: _____________________
THE ESTIMATED DIGIT IS ALWAYS ONE PLACE HOLDER SMALLER THAN THE MARKED INTERVAL IN THE INSTRUMENT.
HUNDREDTHS
THOUSANDTHS
0.270 cm
0.1 0.2 0.3 0.4 0.5 cm
3.1
Significant Figures
5
MARKED POSITION: _____________________
ESTIMATED POSITION: _____________________
MEASUREMENT: _____________________
TENS
ONES
163 mL
100
200
300
mL
200
100
3.1
Daily Challenge 9/16
• Explain the correct way to obtain a measurement with correct significant figures.
Two kinds of numbers:
• Exact numbers – Infinite number of significant figures.– Example: There are exactly 12 eggs in a dozen. – Example: There are exactly 1000 m in 1 km.
• Inexact numbers (any measurement)– Depends on the precision of the instrument.– Example: If I quickly measure the width of a piece of
notebook paper, I might get 220 mm (2 significant figures). If I am more precise, I might get 216 mm (3 significant figures). An even more precise measurement would be 215.6 mm (4 significant figures).
ALL NONZERO DIGITS ARE SIGNIFICANT– 12.5 L HAS 3 SIG. FIGS– 1.254 g HAS 4 SIG. FIGS
Significant Figures Rules
1
ZEROS BETWEEN NONZERO DIGITS ARE SIGNIFICANT– 505 L HAS 3 SIG. FIGS– 4002 g HAS 4 SIG. FIGS
2
3.1
ZEROS THAT APPEAR IN FRONT OF NONZERO DIGITS ARE NOT SIGNIFICANT– 0.0045 L HAS 2 SIG. FIGS– 0.101 g HAS 3 SIG. FIGS
Significant Figures Rules
3
ZEROS AT THE END OF A NUMBER & TO THE RIGHT OF THE DECIMAL POINT ARE SIGNIFICANT– 1.010 L HAS 4 SIG. FIGS– 4.0 g HAS 2 SIG. FIGS
4
3.1
Significant Figures Rules
5 ZEROS AT THE END OF A NUMBER & TO THE LEFT OF THE DECIMAL POINT ARE SIGNIFICANT IF THE DECIMAL IS WRITTEN– 1000 L HAS 1 SIG. FIG– 1000. g HAS 4 SIG. FIGS
3.1
Significant Figures Rules
DEFINED QUANTITIES AND EXACT (NOT MEASURED) NUMBERS HAVE INFINITE SIG FIGS.– π HAS INFINITE SIG. FIGS– 1 DOZEN HAS INFINITE SIG. FIGS
6
3.1
Significant Figures Practice
6 DETERMINE HOW MANY SIG FIGS ARE
IN THE FOLLOWING NUMBERSa. 808 mL ________ b. 9584.02 g ________ c. 124500. cm________ d. 0.01375 L ________ e. 505.0 m ________ f. 1.00 cm3 ________
g. 967 g ________ h. 54,000 g ________
i. 0.08720 g ________ j. 1 mile = 5280 ft ________
3 (2) 6 (2)
6 (5) 4 (3)
4 (2,4) 3 (4)
3 (1) 2 (5)
4 (4) inf (6)
3.1
Daily Challenge 9/20
• Identify how many significant figures are in the following and then round each number to 3 sig figs. 14,501
12.00
0.08976
14010
• ADDITION OR SUBTRACTION– The answer can have no more digits to the
right of the decimal point than there are in the measurement with the smallest number of digits to the right of the decimal point.
3.95 cm
2.879 cm
+ 213.6 cm
Sig Figs in Calculations
220.429 cm 220.4 cm
7
3.1
• ADDITION OR SUBTRACTION– The answer can have no more digits to the
right of the decimal point than there are in the measurement with the smallest number of digits to the right of the decimal point.
14.01 m
2.879 m
- 0.0075 m
Sig Figs in Calculations
11.124 m 11.12 m
7
3.1
3.24 m + 7.0 m
Calculation Calculator says: Answer
10.24 m 10.2 m
100.0 g - 23.73 g 76.27 g 76.3 g
0.02 cm + 2.371 cm 2.391 cm 2.39 cm
713.1 L - 3.872 L 709.228 L 709.2 L
Sig Figs in Calculations
3.1
• MULTIPLICATION OR DIVISION– The answer can have no more significant
figures than there are in the measurement with the smallest number of significant figures.
Sig Figs in Calculations
4.05 cm × 0.0059 cm × 500.0 cm = 11.948 cm3 7(3) (2) (4)(2)
11.948 cm3 → 12 cm3
3.1
• MULTIPLICATION OR DIVISION– The answer can have no more significant
figures than there are in the measurement with the smallest number of significant figures.
Sig Figs in Calculations
12.51 mL ÷ 1000 = 0.01251 mL 7(4) (1)(1)
0.01251 mL → 0.01 mL
3.1
5.87 m × 7.4 m
Calculation Calculator says: Answer
43.438 m2 43 m2
99.74 g ÷ 23.73 4.203118 g 4.203 g
0.02 cm × 2.371 cm 0.177122 cm2 0.2 cm2
710 L ÷ 3.872 183.367 L 180 L
Sig Figs in Calculations
3.1
Daily Challenge 9/21
• Calculate the following and record your answer with correct sig figs – 710 L ÷ 3.872– 0.02 cm + 2.371 cm– 2.36 x 102 mm x 1.6 x 104 mm– 100 g - 23.73 g
SCIENTIFIC NOTATION• A GIVEN NUMBER WRITTEN AS A PRODUCT
OF TWO NUMBERS:
A × 10B
A COEFFICIENT BETWEEN 1 AND 10
A POWER OF 10
3.1
SCIENTIFIC NOTATION• WRITE THE FOLLOWING NUMBERS IN
SCIENTIFIC NOTATION
8 6,200 mA
× 10B
123
6.2 × 103
+ B WHEN DECIMAL MOVES TO THE LEFT
3.1
SCIENTIFIC NOTATION• WRITE THE FOLLOWING NUMBERS IN
SCIENTIFIC NOTATION
8 8,542,000 mA
× 10B
123
8.542 × 106
+ B WHEN DECIMAL MOVES TO THE LEFT
456
3.1
SCIENTIFIC NOTATION• WRITE THE FOLLOWING NUMBERS IN
SCIENTIFIC NOTATION
8 0.002548 mA
× 10B2.548 × 10-3
- B WHEN DECIMAL MOVES TO THE RIGHT
321
3.1
SCIENTIFIC NOTATION• WRITE THE FOLLOWING NUMBERS IN
SCIENTIFIC NOTATION
8 0.00158 mA
× 10B1.58 × 10-3
- B WHEN DECIMAL MOVES TO THE RIGHT
321
3.1
SCIENTIFIC NOTATION• WRITE THE FOLLOWING NUMBERS IN
STANDARD NOTATION
9 2.5 × 10-3 m 0.0025 m
3.1
123
6.45 × 101 s 64.5 s
1
SCIENTIFIC NOTATION• WRITE THE FOLLOWING NUMBERS IN
STANDARD NOTATION
9 4.52 × 104 g 45200 g
3.1
5.25 × 10-2 mL 0.0525 mL
321 4
12
Daily Challenge 9/23
Calculate the following using correct sig figs.
45.60g ÷ 12.0
20.03 g – 15.42 g
7.89 x 1012 mm x 2.2 x 1017mm
Dimensional Analysis
• Problem solving technique
• Involves the study of dimensions of physical quantities
• Used primarily as a tool for obtaining information about physical systems too complicated for full mathematical solutions
S.U.T.S
• S = Starting quantity– Identify only ONE!!!!!
– Recognize it because if you change the starting quantity, you change the answer
– Think…what do you know you have in the beginning? Or what do you want to convert?
S.U.T.S
• U = Unknown Quantity– Identify only ONE!!!!!
– Ending quantity
– Recognize it because as the units you are looking for
– Think…what do you want to find? What units do you want at the end?
S.U.T.S
• T = Transformations– RELATIONSHIPS or SET QUANTITIES – Usually everything else in a problem is a
relationship!!!!!– Use the form A = B
• 1 mol Na = 6.02 x 1023 atoms Na
– Think…what can I use to get from starting to unknown?
S.U.T.S
• S = Set Up & Solve
4.56 mL 10-3 L
10-1 L1 mL
1 dL
Starting Quantity Transformations
Daily Challenge 9/28Daily Challenge 9/28
• Round the following numbers to express 3 sig figs.
– 2147 m
– 20107 mm
– 1300.1 cm
– 400 L
Daily Challenge 9/25
• Gold has sold for $500.0 per ounce. Considering that there are 16 ounces per pound and 454 grams per pound, how many grams of gold could you buy for one cent?
• S:_____________________• U:_____________________• T:_____________________• S:
SUTS Practice
• Michael Scott wants to purchase 3 gallons of blue moon custard. Unfortunately, the custard stand only sells custard by the pints. Determine how many pints Michael would need given the following equalities
• 1 gallon = 4 quarts, 1 tablespoon = 0.0625 cups, 1 quart = 2 pints
INTERNATIONAL SYSTEM OF UNITS
• 1960 INTERNATIONALLY ACCEPTED UNITS FOR MEASUREMENT
3.2
Quantity Unit Symbol
Length meter m
Mass kilogram kg
Time second s
Electric current ampere A
Temperature kelvin K
Amount of substance mol mol
INTERNATIONAL SYSTEM OF UNITS
• Why do we use SI measurements???
• Clearly communicate to one another without having to constantly convert between systems
• Every major nation, with the exception of U.S. have adopted the metric system
• This system is based on the units of ten
METRIC PREFIXES
• PREFIXES ARE USED TO MODIFY UNITS TO MATCH THE SIZE OF AN OBJECT
• Giga billion 10-9 Gm = 1 m• Mega million 10-6 Mm = 1 m• kilo thousand 10-3 km = 1
m• Base (meters)• deci tenth 101 dm = 1 m• centi hundredth 102 cm = 1 m• milli thousandth 103 mm = 1 m• micro millionth 106 µm = 1 m• nano billionth 109nm = 1 m
3.2
METRIC PREFIX CONVERSIONS
• KNOWING THE MEANING OF A PREFIX ALLOWS US TO CONVERT BETWEEN UNITS
1 CONVERT 4.25 mm TO m
U
T
S
STARTING MEASUREMENT
UNKNOW MEASUREMENT
TABLE TRANSFORMATION
SET-UP & SOLVE3.2
METRIC PREFIX CONVERSIONS
1 CONVERT 4.25 mm TO m
S
U
T
S
4.25 mm
# m
______ mm = ______ m103 1
4.25 mm
mmm
103
1
4.25 mmmm
m103
1× = 0.00425 m3.2
PREFIX TO BASE
1 TRANSFORMATION!!
METRIC PREFIX CONVERSIONS
1 CONVERT 78.1 kg TO g
S
U
T
S
78.1 kg
# g
______ g = ______ kg1 10-3
78.1 kg
kgg
10-3
1
78.1 kgkgg
10-3
1× = 78100 g3.2
PREFIX TO BASE
1 TRANSFORMATION!!
METRIC PREFIX CONVERSIONS
1 CONVERT 0.045 s TO μs
S
U
T
S
0.045 s
# μs
______ μs = ______ s106 1
0.045 s
sμs
1106
0.045 ssμs
1106
× = 4.5 × 104 μs3.2
BASE TO PREFIX
1 TRANSFORMATION!!
CONVERSIONS
1 CONVERT 4.25 cal TO J
S
U
T
S
4.25 cal
# J
1 J = 0.2390 cal
3.2
4.25 cal
calJ
0.23901
4.25 calcalJ
0.23901× = 17.8 J
UNIT TO UNIT
TEMPERATURE CONVERSIONS
• Three temperature scales– Fahrenheit (⁰F)– Celsius (⁰C)– Kelvin (K)
• ⁰F = (9/5) ⁰C + 32
• ⁰C = (5/9) x (⁰F – 32)
• K = ⁰C + 273
CONVERSIONS
1 CONVERT 50 °C TO K
S
U
T
S
50 °C
# K
K = °C + 273
3.2
K = °C + 273
K = 50 + 273 = 323 K
Daily Challenge 9/29
• A common pain reliever contains 500mg per tablet. Package direction recommend taking no more than 8 tablets in a 24hr period. how many grams of this pain reliever a day is the maximum recommended dose?
• S• U• T• S
METRIC PREFIX CONVERSIONS
2 CONVERT 25.2 nm TO mm
S
U
T
S
25.2 nm
# mm
______ nm = _______ m1109
3.2
______ mm = ______ m1103
S
PREFIX TO PREFIX
2 TRANSFORMATIONS!!
25.2 nm
nmm1
109 m
103
1mm
= 2.52 × 10-5 mm
METRIC PREFIX CONVERSIONS
2 CONVERT 4.1×107 nA TO cA
S
U
T
S
4.1×107 nA
# cA
______ nA = ______ A1109
3.2
______ cA = ______ A1102
S
PREFIX TO PREFIX
2 TRANSFORMATIONS!!
4.1×107 nA
nAA1
109 A
102
1cA = 4.1 cA
METRIC PREFIX CONVERSIONS
2 CONVERT 8.57 dK TO kK
S
U
T
S
8.57 dK
# kK
______ dK = ______ K1101
3.2
______ kK = ______ K110-3
S
PREFIX TO PREFIX
2 TRANSFORMATIONS!!
8.57 dK
dKK1
101 K
10-3
1kK = 8.57 × 10-4 kK
Daily Challenge 10/4
• Many candy bars have 9 g of fat per bar. During a typical month an individual eats three candy bars. How many ounces of fat does this person eat per year if there are 28.35 grams in an ounce?
DENSITY
• It is the ratio of the mass of an object to its volume
• It is a CONVERSION FACTOR!!!! or in other words a RELATIONSHIP!!!!
• Density = mass
volume
DENSITY
• It is an INTENSIVE PROPERTY
• Depends only on the COMPOSITION of a substance, NOT the SIZE of the sample
• Density of a substance generally decreases as its temperature increases.
• D T
DENSITY
• The density equation gives you the equality between mass and volume.– Ex. Density of gold = 19.2 g/mL
• NOTE: 1mL = 1 cm3
19.2g of gold = 1 mL of gold
DENSITY
• Convert 14.8 g of boron to cm3 using the density of boron (2.34 g/cm3)
• 4.62 g or mercury to cm3 using the density of mercury (13.5 g/ cm3)
DENSITY
• You may also need to convert units within density.
• Take note of where units are!!!
• Convert 4.56 g/mL to g/dL
4.56 g
1 mL
1 mL 10-1 L
10-3 L 1 dL= 4.56 x 102 dL
Practice…• 3.0 x 102 ms to ns
• 6.74 x 107 km/s to cm/ds
• 8963 mm/cA to m/nA
• 19.7 g/mL to kg/L
• 1.33 g/cm3 to mg/L
Significant Figures Practice
• Express each number to 4 significant figures:– 248.694
• 248.7
– 5006.8 • 5007
– 0.0014581 • 1.458 x 10-3
– 800.06 • 800.1
Significant Figures Review
• Determine the number of significant figures in:– 8904
• 4 significant figures
– 0.0541• 3 significant figures
– 102.50• 5 significant figures
– 500• 1 significant figure
Significant Figures Practice
• Express your answer to the correct number of significant figures– 52.17 m + 32.0 m
• 84.2 m
– 500.0 lbs + 73.24 lbs• 573.2 lbs
– 90210.45 mL – 53186 mL• 37024 mL
– 53.1 g – 2.4589 g• 50.6 g
Practice Measurements
• Marked Interval?– Tens position
• Estimated Position?– Ones position
• Measurement?– 12 m– 2 estimated and significant
● 5 63 4
Ten
s One
s
Ten
ths
Hun
dred
ths
10 20 30 40m
• In your class notes notebook
• For each station– Write the marked interval– Write the estimated interval– Make the measurement with appropriate units
(mL, g, s)
Measurements Lab
Helpful Web Pages
• http://science.widener.edu/svb/tutorial/sigfigures.html
SI UnitsSI Units
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