1. UNITS & DIMENSIONAL ANALYSIS (conversions)
UNIT 2-MEASUREMENTS
UNITS &
DIMENSIONAL ANALYSIS
(conversions)

2. Number vs. Quantity A number without a unit is a “naked” number
Quantity - number + unit
UNITS MATTER!!

3. Common SI Units Quantity Symbol Base Unit Abbrev. Length l meter m
Volume v
Liter L
Mass m
kilogram kg
Time t
second s
Temp T
kelvin K
Amount n
mole
mol

4. SI Units
Base units:
*Mass : grams  g
Volume: Liters  L
Length: meters  m

5. SI Prefixs Prefix Symbol Factor mega- M 106 kilo- k 103 BASE UNIT ---
100
deci- d
10-1
move left
move right
centi- c
10-2
milli- m
10-3
micro- 
10-6
nano- n
10-9
pico- p
10-12

6. SI Prefixes K  Kilo Kangaroos H  Hecta Have D  Deka Dark U 
m 
Kilo
Hecta
Deka
Unit (base)
deci
centi
milli
Kangaroos
Have
Dark
Umbrellas
during
cloudy
mornings

7. SI Conversions (short-cut)
K H D U d c m
Count the number of places you have to move left or right.
Move the decimal that many places left or right.
To the left
or right?

8. SI Conversions (short-cut)
532 m = _______ km
0.532
K H D U d c m

9. SI Conversions (short-cut)
0.2
1) 20 cm = ______________ m
2) L = ______________ mL
3) 45 kg = ______________ g
4) 805 dm = ______________ m 32
45,000
80.5

10. Not all conversions can use the short-cut…. Hang on tight
Not all conversions can use the short-cut…. Hang on tight!! We’re going for a ride!

11. A fancy word that means conversions
Dimensional Analysis
A fancy word that means conversions

12. Dimensional Analysis The “Factor-Label” Method:
A method used to “factor” out (cancel) labels (units)

13. Dimensional Analysis 10 days 24 hrs 1 day = 240 hrs
How many hours are in 10 days?
-what info do you need to know first?
- 24 hours in 1 day
10 days
24 hrs
1 day
= 240 hrs 

14. = 1 = 1 Dimensional Analysis Ex: 1 kg 1000 g
Conversion Factor: any ratio that equals one, used in converting
Ex: 4 quarters
1 dollar
= 1
Ex: 1 kg
1000 g
= 1

15. Dimensional Analysis Steps: 1. Identify starting & ending units.
2. Line up conversion factors so units cancel.
3. Multiply all top numbers & divide by each bottom number.
4. Check units & answer.

16. Dimensional Analysis hrs How many seconds are in 36 hrs? s 36 hrs
60 min
1 hr
60 sec
1 min
= 129,600 sec 

17. Dimensional Analysis 550 cm 1 in 2.54 cm 1 ft 12 in 1 yd 3 ft = 6.0 yd
Brandeis football needs 550 cm for a 1st down. How many yards is this? cm yd
550 cm
1 in
2.54 cm
1 ft
12 in
1 yd
3 ft
= 6.0 yd

18. Dimensional Analysis
A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire? cm
pieces
1.3 m
100 cm
1 m
1 piece
1.5 cm
= 86 pieces

19. m v D Density D = m / v Remember to cover up what you want
In order to find
the equation
D = m / v D m v

20. D = m/v m D v Density Formula: Units: Mass = g (grams)
Volume = mL or cm3
Density = g/mL or g/cm3
REMEMBER TO COVER UP
THE UNIT THAT YOU WANT
IN ORDER TO FIND
D = m/v D m v

21. Density
Mass (g)
Volume (cm3)

22. M V D = Derived Units 1 cm3 = 1 mL 1 dm3 = 1 L
A Combination of base units. For example:
Volume (m3 or cm3)
length  length  length
1 cm3 = 1 mL
1 dm3 = 1 L
Density (kg/m3 or g/cm3)
mass per volume
D = M V

23. D. Density m D v V = 825 cm3 M = DV D = 13.6 g/cm3
An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
M = ?
WORK:
M = DV
M = (13.6 g/cm3)(825cm3)
M = 11,200 g D m v

24. D. Density m D v D = 0.87 g/mL V = M V = ? M = 25 g V = 25 g 0.87 g/mL
A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?
GIVEN:
D = 0.87 g/mL
V = ?
M = 25 g
WORK:
V = M D
V = g
0.87 g/mL D m v
V = 29 mL