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Scientific Notation
 1,000,000 = 1 million
Scientific Notation
 1,ooo,ooo = 1 million = 1 x 106
Move the decimal point to a
value between 1 and 10
1 000 000. ------> 1 x 106
Move the
Decimal 6 places to the
left
Scientific Notation
 There are 0.0000001 H+
ions in a neutral solution
Scientific Notation
 There are 0.0000001 H+
ions in a neutral solution
= 1 x 10-7
H+
ions
Scientific Notation
 Format:
450,000 = 4.5 x 105
0.000073 = 7.3 x 10-5
Number between
1 and 9.99
Power of Ten
10 x 10 x 10 x . . .x
Scientific Notation
 NaCl crystal
Distance Na+
.. Cl–
0.000000000278 m
Scientific Notation
 NaCl crystal
Distance Na+
.. Cl–
0.000000000278 m
= 2.78 x 10-10
m
Scientific Notation
 US National Debt (2016)
$18, 200,000,000,000
Scientific Notation
 US National Debt (2016)
$18, 200,000,000,000
= $1.82 x 1013
Scientific Notation
 Scientific calculators
 8.978+01 = 8.978 x 101
= 89.78
5.0627 E+15
= 5.0627 x 1015
= 5,062,700,000,000,000
Significant Figures
 How do you know how many decimal places to use?
 All of the digits known with certainty plus one
estimated digit.
Significant Figures
Rules
 Any non-zero digit is Significant
 Any zero between non-zero digits is Significant
 All zeros to the left of the first non-zero digit are
NOT Significant
 Zeros after the decimal point are Significant
 Zeros that occur without a decimal point are NOT
significant
Significant Figures
 How many significant figures does each value have?
Value # Significant figures
0.00008 m
36,000 km
22.00 g
5.05 x 10-3
mg
Significant Figures
 How many significant figures does each value have?
Value # Significant figures
0.00008 m 1
36,000 km 2
22.00 g 4
5.05 x 10-3
mg 3
Significant Figures
 When multiplying or dividing, the result cannot have
more sig figs than either of the original values
 In addition or subtraction, the answer cannot have
digits after the decimal than the original values
 Rounding: If the first digit to be dropped is 4 or less,
the last digit and any following are dropped. If the
last digit is 5 or more, the last digit is kept and
increased by 1.
Significant Figures
 A 2002 Toyota Camry uses 11.70 gallons of gas to
travel 278 miles – what is its mileage?
Significant Figures
 A 2002 Toyota Camry uses 11.70 gallons of gas to
travel 278 miles – what is its mileage?
3 sig figs
278 miles = 23.8 mi/gal
11.7ogallons
3 sig figs
4 sig figs
Significant Figures
 A 2002 Toyota Camry uses 11.70 gallons of gas to
travel 278 miles – what is its mileage?
3 sig figs
278 miles = 23.8 mi/gal
11.7ogallons
3 sig figs
4 sig figs
The answer CANNOT have more significant figures than the
input value with LESS sig figs.
Significant Figures
Significant Figures
 Blood cholesterol level = 185 mg/dL
= ?? g/L
How many g of
cholesterol are in 5 Liters
Of blood?
Significant Figures
 Blood cholesterol level = 185 mg/dL x g/1000mg x 10dL/L
= 1.85 g/L
How many g of
cholesterol are in 5L blood?
1.85 g/L x 5 L
= 9.25 g = 9 g
The answer is limited to 1 sig fig
Density
 Archimedes
confirmed that a crown was
made of gold rather than
gold-covered metal by measuring
its density by water displacement
mass
Density =
volume
Density
 A piece of lead measures 0.5 cm x 1.55 cm x 25 cm
and has a mass of 220.9 grams – what is its density?
Density
 A piece of lead measures 0.50 cm x 1.55 cm x 25 cm
and has a mass of 220.9 grams – what is its density?
mass
Density = volume
220.9g
= 19.38 cm3
= 11.40 g/cm3
= 11 g/cm3
[2 sig figs]
Bone Density
 Decreases with age (Osteoporosis)
Normal
weakened
mg
cm3
Body Mass Index (BMI)
Density & Temperature
 Density measurement must include temperature
phase changes
Temperature
 Temperature is a measure of the amount of Kinetic
Energy in a substance
 Kinetic Energy = Energy of motion
 http://phet.colorado.edu/en/simulation/states-of-
matter
Temperature Scales
°C = (°F – 32) x 0.55
°F = (°C x 1.8) + 32
K = °C +273
Temperature Scales
°F °C K
57°F
-75°C
6
106°F
°C = (°F – 32) x 0.55
°F = (°C x 1.8) + 32°
K = °C +273
Temperature Scales
°F °C K
57°F 14°C 287 K
-103°F -75°C 198 K
-449°F -267°C 6
106°F 41°C 314 K
°C = (°F – 32°) x 0.55
°F = (°C x 1.8) + 32°
K = °C +273°
States of Matter
melting
Freezing
evaporating
condensing
Phase Changes
Boiling Point
 For water Tb = 100°C = 373 K
Freezing Point
 For water, Tf = 0°C = 273K
Heating & Cooling Curves
Heat of Fusion
 Energy necessary to separate particles
For water: 80 cal/g
Heat of Fusion
 Ice cube tray hold 325 g water. If the water is
originally at 25°C how many calories must be
removed to cool and freeze the water at 0°C?
Heat of Fusion
 Ice cube tray hold 325 g water. If the water is originally at 25°C
how many calories must be removed to cool and freeze the
water at 0°C?
 Cooling:
325 g x 1 cal/g°C x 25°C = 8125 cal
• Freezing:
325 g x 80cal/g = 26000 cal
TOTAL: 34125 cal = 34.125 kilocalories
Heat of Vaporization
 Energy to vaporize 1 g of liquid to gas
 Water: 540 cal/g
Steam vs. Hot Water
 Why does steam burn more than hot water at the
same temperature? (100°C) body temp = 37°C
 Hot water:
25 g x 63°C x 1 cal/g°C = 1575 cal
Steam:
25 g x 540 cal/g = 13500 cal
TOTAL: 15075 cal (10x that of hot water)

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