Daily Challenge 9/16

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


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


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


MARKED POSITION: _____________________


MEASUREMENT: _____________________


ONES

TENTHS

2.5 cm

1 2 3 4 cm

3.1

Significant Figures

4


MARKED POSITION: _____________________


MEASUREMENT: _____________________


HUNDREDTHS

THOUSANDTHS

0.270 cm

0.1 0.2 0.3 0.4 0.5 cm

3.1

Significant Figures

5

MARKED POSITION: _____________________


MEASUREMENT: _____________________

TENS

ONES

163 mL

100

200

300

mL

200

100

3.1


• 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


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


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


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


• 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


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


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.


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.


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


3.1


• 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

8 8,542,000 mA

× 10B

123

8.542 × 106

+ B WHEN DECIMAL MOVES TO THE LEFT

456

3.1


SCIENTIFIC NOTATION

8 0.002548 mA

× 10B2.548 × 10-3

- B WHEN DECIMAL MOVES TO THE RIGHT

321

3.1


SCIENTIFIC NOTATION

8 0.00158 mA

× 10B1.58 × 10-3

- B WHEN DECIMAL MOVES TO THE RIGHT

321

3.1


STANDARD NOTATION

9 2.5 × 10-3 m 0.0025 m

3.1

123

6.45 × 101 s 64.5 s

1


STANDARD NOTATION

9 4.52 × 104 g 45200 g

3.1

5.25 × 10-2 mL 0.0525 mL

321 4

12


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


• 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


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!!


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!!


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


• 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


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


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


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


• 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


• 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


• 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

http://science.widener.edu/svb/tutorial/sigfigures.html

http://science.widener.edu/svb/tutorial/sigfigures.html

SI UnitsSI Units

Daily Challenge 9/16

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Transcript of Daily Challenge 9/16