1. DIMENSIONAL ANALYSIS
Problem solving using equalities
How many Japanese yen can you get for $5.00?
An EQUALITY STATEMENT between yen and dollars is needed
$1.00 = ¥113
An equality statement can be written as a fraction called a CONVERSION FACTOR
$1.00
_______
¥113
¥113
_______
$1.00
$5.00
x ¥113
________
$1.00
= ¥565 or
1B-1 (of 24) (2 – ) (3 – )

2. How many British pounds can you get for $5.00?
£1.00 = $1.30
£1.00
_______
$1.30
$1.30
_______
£1.00
$5.00
x £1.00
________
$1.30
= £3.85 or
1B-2

3. How many Japanese yen can you get for 5.00 British pounds?
Equality statement between ¥ and £? No
£1.00 = $1.30
$1.00 = ¥113
£5.00
x $1.30
________
£1.00
x ¥113
________
$1.00
= ¥735
1B-3

4. How many miles are in 1,000,000. inches?
1 ft = 12 in
1 mi = 5,280 ft
1,000,000. in
x ft
_______
12 in
x mi
__________
5,280 ft
= mi
1B-4

5. How many seconds are in 1.0000 year?
1 yr = 365 dy
1 dy = 24 h
1 h = 60 min
1 min = 60 s yr
x dy
________
1 yr
x h
_______
1 dy
x min
_________
1 h
x s
________
1 min
= ,536,000 s
1B-5

6. How many cubic yards of air are in 18 cubic feet of air?
1 yd = 3 ft
1 yd3 ≠ 3 ft3
(1 yd)3 = (3 ft)3
1 yd3 = 27 ft3
18 ft3
x 1 yd3
________
27 ft3
= yd3
1B-6

7. Convert 35 mi/h into ft/min
1 mi = 5,280 ft
1 h = 60 min
35 mi
________ h
x 5,280 ft
__________
1 mi
x h
_________
60 min
= 3,080 ft/min
= 3,100 ft/min
1B-7

8. TEMPERATURE SCALES
TEMPERATURE – A property of a system based upon the average energy of the particles making up the system
Two common temperature scales are the Fahrenheit and Celsius scales
1B-8

9. y = mx b
ºF = mºC + b
← Boiling point of water
m =
__________
= 9
___ 5
°F = 9 °C + b __ 5
← Room Temperature
← Freezing point of water
32 = 9 (0) + b __ 5
32 = b
ºF = 9 ºC __ 5
1B-9

10. What is the Celsius temperature when it is 95ºF?
ºF = 9 ºC __ 5
ºF = 9 ºC __ 5
5 (ºF ) = ºC __ 9
5 ( ) = __ 9
35ºC
1B-10

11. Scientists believe there is a lowest possible temperature
ABSOLUTE SCALE – A scale with 0 as its lowest possible value
The Kelvin scale is an absolute scale
← Boiling point of water
: -273ºC
← Freezing point of water
K = ºC
← Absolute Zero
1B-11

12. METRIC CONVERSIONS
METRIC PREFIXES
Prefix Symbol BUMF
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
1B-12

13. How many kilometers are 525 meters?
1 BIG km = 103 small m
METRIC PREFIXES
Prefix Symbol BUMF
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
1 km
_______
103 m
103 m
_______
1 km or
525 m
x km
________
103 m
= km
1B-13

14. How many centigrams are 8.93 grams?
1 BIG g = 102 small cg
METRIC PREFIXES
Prefix Symbol BUMF
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
8.93 g
x cg
________
1 g
= cg
How many liters are 25.0 milliliters?
1 L = 103 mL
25.0 mL
x L
________
103 mL
= L
1B-14

15. How many kilograms are 150 decigrams?
1 BIG kg = 104 small dg
METRIC PREFIXES
Prefix Symbol BUMF
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
150 dg
x kg
________
104 dg
= kg
1B-15

16. How many micrometers are 0.37 centimeters?
1 BIG cm = 104 small μm
METRIC PREFIXES
Prefix Symbol BUMF
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
0.37 cm
x μm
_________
1 cm
= 3,700 μm
1B-16

17. Convert 22.5 mL/s into L/min
1 mL = 10-3 L
1 min = 60 s
METRIC PREFIXES
Prefix Symbol BUMF
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
22.5 mL
___________ s
x L
________
1 mL
x s
________
1 min
= L/min
1B-17

18. Convert 25.0 m/h into cm/min
1 h = 60 min
METRIC PREFIXES
Prefix Symbol BUMF
mega M 106
kilo k 103
BASE UNIT 100
deci d 10-1
centi c 10-2
milli m 10-3
micro μ 10-6
nano n 10-9
25.0 m
___________ h
x cm
________
1 m
x h
_________
60 min
= cm/min
1B-18

19. THE PROPERTY OF DENSITY
Material Density
Lead
Water
Cork
Air
Helium
11.34 g/mL
1.00 g/mL
0.24 g/mL
g/mL
g/mL
DENSITY – Mass per unit volume
D = m
___ V
1B-19

20. What is the density of a solid in which 2.20 g occupies 1.50 mL?
D = m
___ V
= g
__________
1.50 mL
= g/mL
1B-20

21. What is the mass of 12. 0 mL of a solid if it has a density of 3
What is the mass of 12.0 mL of a solid if it has a density of 3.50 g/mL?
D = m
____ V
VD = m
= (12.0 mL)(3.50 g/mL)
= g
1B-21

22. What volume does 6.2 g of a liquid occupy if its density is 1.4 g/mL?
D = m
____ V
VD = m
V = m
____ D
= g
____________
1.4 g/mL
= mL
1B-22

23. REVIEW FOR TEST
Identify laboratory equipment
Location of safety equipment
Accuracy of graduated glassware
Safety procedures
Scientific notation
Reading graduated equipment
Significant figures
Operations with significant figures
1B-23

24. REVIEW FOR TEST
Metric prefixes
Dimensional analysis
Know metric and time equalities
Temperature scales
Know equalities between them
Density
Solve for D, m, or V
1B-24