measurement
DESCRIPTION
Measurement. Scientific Notation. Used for numbers that are really big or really small. A number in exponential form consists of a coefficient multiplied by a power of 10. 1 x 10 4. 10,000 1,000,000 546,000 0.00001 0.00751. 0.00000029 12,450 15,230,000 0.0884. 2.9 x 10 -7. - PowerPoint PPT PresentationTRANSCRIPT
Scientific NotationUsed for numbers that are really big or really small
A number in exponential form consists of a coefficient multiplied by a power of 10
10,000
1,000,000
546,000
0.00001
0.00751
0.00000029
12,450
15,230,000
0.0884
1 x 104
1 x 106
5.46 x 105
1 X 10-5
7.51 x 10-3
2.9 x 10-7
1.245 x 104
1.523 x 107
8.84 x 10-2
If the coefficient does not fall between 1 and 10 , it must be re-written correctly
If you move the decimal to the right, subtract from the exponent
If you move the decimal to the left, add to the exponent 100 x 103
0.0001 x 1012
4,490 x 10-
7
0.0065 x 103
0.090 x 10-5
0.0112 x 108
150 X 1012
200 x 10-2
1 X 105
1 X 108
4.49 x 10-4
6.5 x 100 = 6.5
9 X 10 -7
1.12 x 106
1.5 x 1014
2 X 100
calculations involving scientific notation
Enter the coefficient, then EE or ExpDo not enter “x
10”
(2.4 x 106) (3.1 x 103 ) =
(9.5 x 10-7) (5 x 10-4 ) =
4.8 x 109 = 2.4 x 102
7.5 x 10-5 + 4.2 x 10-6 =
7.44 x 109
4.75 x 10-10
2 X 107
7.92 x 10-5
Two types of dataQualitati
vedescriptiveEx: the burner flame is hot
Quantitative numerical Ex: the flame is
1000 ° CMeasurements should be both accurate and precise
Accuracyhow close the experimental value is to the accepted or true value
calculating percent error
% E = |accepted –experimental|accepted
X 100
Precisionhow close the measurements are to each other when the experiment is repeated
Ex: a student does an experiment todetermine the density of lead; she repeatsthe experiment two more times and getsthese results:
10.1 g/cm3 9.4 g/cm3 and 8.5 g/cm3
comment on her precision
If the actual density of lead is 11.4 g/cm3, calculate her percent error using her average density as the experimental value
poor
|11.4 – 9.3|% E =
11.4100 = 18.4 %Avg.= 9.3
Mass (weight)
Quantities and their units
gram (g)kilogram (kg) milligram (mg)
Length (distanc
e)
meter (m)kilometer
(km)millimeter
(mm)
Example units
Volume liter (L)milliliter (ml)any unit of length that is cubed
1 mL = cm3
1m
1 m
1 m
Vol. = L x W x H
Vol. = 1 m3
Temperature
Celsius, ° C Kelvin, K
HeatJoules (J)Calorie (Cal)
number of
particles
mole
1 mole = 6.02 x 1023
Metric Conversionsuse dimensional analysis to convert between these units
1. 12 inches = ? cm 1 in. = 2.54 cm
in.
cm12 in.
1
2.5430.48 cm
2. 95 miles = ? km 1 km = 0.62 mi
3. 400 lbs. = ? kg 1 kg = 2.2 lbs
4. 250 grams = ? oz.1 oz = 28 g
95mi
mi
km
lbs
lbs
kg
g
g
oz
1
0.62
400
2.2
1
250
28
1
153 km
182 kg
8.9 oz
5. 500 cm = ? in.1 in. = 2.54 cm
kilo (k)
1000 times larger
10 times smaller (1/10)
centi (c)
deci (d)
100 times smaller (1/100)
500 cmcm
in
2.54
1197 in
milli(m) 1000 times smaller (1/1000)
micro (µ)
1 x 106 times smaller(1/106)
nano (n)
1 x 109 times smaller(1/109)
Ex: 5 m = ? cm
5 m
m
cm
1
100500 cm
1.50 L = ? mL
1 X 103 dg = ? g
0.025 g
1500 mL
Ex: 25 mg = ? g
25
mg
g
1000
1mg
1.50
L
mL
1
1000L
1x 103 dg
g
10
1dg100 g
2.4 g = ? cg
3 X 1012 µg = ? g
0.9 dm = m
2.4 g
g
cg
1
100240 cg
3 x 1012µg
µg
g
1 X 106
13 X 106 g
0.9dm
dm
m
10
10.09 m
7.7 x 105 µm = ? m
200 g = ? kg
7.7 x 105 µm
µm
m1
1 X 1060.77 m
200 g
g0.2 kg
kg1
1000
0.25 L = ? mL
0.25 L
L
ml1000
1250 mL
3.5 x 10-4 g = ? mg
800 µL = L
200 m = ? cm
200 m
m1
cm10020,000 cm
3.5 x 10-4 g
g1
mg1000 0.35 mg
800 µL
1 x106
L10.0008 dL
µL
Significant Figuresall the numbers in a measurement that are knownwith certainty plus one that is estimated
6.3 6.4
6.35
uncertain
3 sig figs
6.3500
incorrect
Rules for determining which numbers in a measurement are significant figures
1. Any number in a measurement that is not zero is
a significant figureEx: 213.5 m has
412, 567 m has
52. Zeros between nonzero numbers are significant figures
Ex: 205 g has 3 10.0002 g has 63. Zeros to the left of a number are not
significant figures
Ex: 0.078 L has 2 0.00005 has 1
4. Zeros to the right of a number and to the right of the decimal are significant figures
Ex: 2.00 has 3 0.00100 has 35.Zeros at the end of a number are not significant figures unless the decimal point is shownEx: 1200 has
21200. has 4
For numbers in exponential form, look only at the coefficient and not the exponent
4.50 x 108 has 3
Identify the number of significant figures in each measurement:
1.______ 250 9.______ 13,979
2.______ 35,029 10.______ 3.00 x 102
3.______ 0.0075 11.______ 0.6000
4. ______ 9000 12.______ 50.
5.______ 0.0080 13.______ 4500
6.______ 10.00 14.______ 0.002
7._______ 3.6 x 105 15.______ 3.040
8._______ 15,000
2
5
2
1
2
4
2
2
5
3
4
2
2
1
4
Rounding off numbersBegin counting from the first significant figure on the left; ifthe number being left off is 5 or higher, round up.
Ex: round 65.31890 to 3 sig figs: 65.3
round 0.05981 to 3 sig figs0.0598
round 43,925 to 2 sig figs44,000 or 4.4 x 104
round 545,858 to 4 sig figs545,900 or 5.459 x 105
round 9.9992 x 10-4 to 2 sig figs1.0 x 10-3
Round each number to 3 sig figs, then to 2 then 1 sig fig
1. 6.77510
2. 0.04031
3. 18.298
4. 0.0011299
5. 892.153
6. 57,320
6.78 6.8 7
18.3 18 20
0.00113 0.0011 0.001
892 890 900
57,320 57,000 60,000
0.0403 0.040 0.04
When rounding off the answer after a calculation,the answer cannot be more accurate than your least accurate measurement
Multiplication and Division
Rule: The number of sig figs in the answer
is determined by the number with the
fewest sig figs
Ex: 1.33 x 5.7 =
0.153 = 0.08
(5.00 x 103) ( 7.2598 x 102) =
7.581 = 7.6
21.9125 =
3.6299 x 106 =
3.63 x 106
Perform each calculation and round to the correctnumber of significant figures
1. 520 x 367 =
2. 2.5 x 9.821 =
3. 0.02430 = 0.95880
4. 4 x 10-8 =
1.5 x 10-2
190,840 = 190,000 or 1.9 x 105
24.5525 = 25
0.02534418 = 0.02534
2.6666 x 10-6 = 3 X 10-6
Addition and Subtraction
Rule: The number of decimal places in the answer is determined by the number with the fewest decimal places
Ex: 10.25 + 11.1 =
515.3215 - 30.42 =
1425 - 820.95 =
21.35 =
484.9015 =
604.05 =
21.4
484.90
604
Perform each calculation and round off tothe correct number of significant figures
1. 20.5 + 8.263 =
2. 0.88 + 3.104 =
3. 0.005 + 0.0066 =
4. 2291.7 - 1512.015 =
28.763 =
3.984 =
0.0116 =
779.685 =
28.8
3.98
0.012
779.7
Density:Ratio of an object’s mass to its volume
Density of water = 1 g/mL or 1 g/cm3
Which is more dense: the water in a tub or in a small cup ? both water
samples have the same density
Sample problems
Calculate the density of a liquid if 50 mL of the liquid weighs 46.25 grams.
D = M V
D = 46.25 g50 mL
0.925
0.9 g/mL
A block of metal has the dimensions: 2.55 cm x 2.55 cm x 4.80 cm.If the mass of the block is 234.61 g, what is the density?V = L x W x HV = (2.55 cm)(2.55 cm)(4.80 cm)
V = 31.212 cm3
D = 234.61 g 7.516667.52 g/cm3
31.212 cm3
A marble weighing53.87 g is placed in agraduated cylindercontaining 40.0 mL ofwater. If the water risesto 64.9 mL, what is the density of the marble?
V= 64.9 – 40.0 =
24.9 mL
D = 53.87 g
24.9 mL2.16345 2.16 g/mL
1.
Calculate the mass of a piece of aluminum having avolume of 8.45 cm3. The density of aluminum is 2.7 g/cm3
(8.45 cm3)D = M V M= D x V
M = (2.7 g/cm3)22.815 23 g
What volume of mercury weighs 25.0 grams?Density of mercury = 13.6 g/mL
D = M V M= D x V V =
M DV = 25.0 g
13.6 g/mLV = 1.838235 1.84 mL
1. What mass of gold (density= 19.3 g/cm3) has a volume of 12.80 cm3 ?
D = M V M= D x VM = (19.3 g/cm3)(12.80 cm3)
M= 247.04 = 247 g
2. Calculate the volume of a cork if its mass is 2.79 grams and it has a density of 0.25 g/cm3
D = M V M= D x V V =
M DV = 2.79 g
0.25 g/cm3
11.16 = 11 cm3
3 scales
B.P. water
F.P. water
AndersCelsius
LordKelvin
Celsius Scale:
Water freezes at 0°C , boils at 100°C
Kelvin Scale:Water freezes at 273 K and boils at 373 K
Absolute Zero: Lowest temperature that can be
reached; all molecular motion stopsK = °C +
273
0 Kelvin
Ex: 25 ° C = ? K
298 K37 °C = ? K
310 K-50 °C = ? K
223 K
0 K = ?°C-273 °C
600 K = ? °C327°C
Heat
Energy that flows from a region of higher tempto lower temp
units: Joules (J) , Calories (Cal)
Specific Heat Capacity: C,
A measure of how wellsomething stores heat
specific heat of water: 1.00 Cal/g°C
1 Cal = 4.18 J
or 4.18 J/g°C
high compared to most substances; water heats upslowly and cools off slowly.
Heat Calculations: q = mCΔTheat
mass
tempchange
specific heat
ProblemsHow many Joules of heat energy are needed to raise the temperature of 50.0 grams of water from 24.5°C to 75.0°C ? specific heat of water = 4.18 J/g °C
q= mCΔT
m
ΔTC
q = (50.0 g) (75.0 – 24.5) (4.18 J/g°C)
50.5°Cq = 10,554.5 10, 600 J
A piece of gold weighing 28 grams cools from 125°C to 23°C. To do this it must lose 362 Joules of heat energy. Calculate the specific heat of gold.
q= mCΔT q= mCΔT
mΔTmΔT
C = q m ΔT
C = 362 J
28 g125- 23
102°C
C = 0.12675 0.13 J/g°C
What mass of graphite can be heated from 30°C to 80°C by the addition of 1500 Joules of heat?Specific heat of graphite = 0.709 J/g°C
q= mCΔT q= mCΔT
CΔTCΔT
m = q CΔT
m = 1500 J
(0.709 J/g°C)(80-30)
50°C
42.3131
40 g
1. How many Joules of heat are needed to increase the temperature of 100.0 grams of iron metal by 80.0°C? specific heat of iron = 0.45 J/g°C
q = (100.0 g)(0.45 J/g°C)(80.0°C)
q= 3600 J
2. 25 grams of water absorb 150 calories of heat. What will be the temp change of the water?
T= q mC
150 Cal______(25 g)(1.00 Cal/g °C) 6°C
q= mCΔT