I

II

III

III. Also called the Factor-Label Method for solving problems

Dimensional Analysis

A. SI Prefix Conversions

1. Find the difference between the exponents of the two prefixes.

2. Move the decimal that many places.

To the leftor right?

=

A. SI Prefix Conversions

NUMBERUNIT

NUMBER

UNIT

532 m = _______ km0.532

A. SI Prefix Conversions

mega- M 106

deci- d 10-1

centi- c 10-2

milli- m 10-3

Prefix Symbol Factor

micro- 10-6

nano- n 10-9

pico- p 10-12

kilo- k 103

mov

e le

ftm

ove

right

BASE UNIT --- 100

A. SI Prefix Conversions

1) 20 cm = ______________ m

2) 0.032 L = ______________ mL

3) 45 m = ______________ nm

4) 805 dm = ______________ km

0.2

0.0805

45,000

32

33

cmgcm

B. Dimensional Analysis The “Factor-Label” Method=

A method of using units (labels, dimensions) to analyze and solve word problems

–Cancel out units (dimensions)!

g

B. Dimensional Analysis Steps:

1. Identify the final units of the answer(and necessary equalities)

2. Start by writing the given (magnitude and dimension)

3. Cancel units using conversion factor equalities(the numerator must equal denominator)

4. Multiply all top numbers & divide by each bottom number.(calculate the numbers!)

B. Dimensional Analysis Lining up conversion factors:

1 in = 2.54 cm2.54 cm 2.54 cm

1 in = 2.54 cm 1 in 1 in

= 1

1 =

B. Dimensional Analysis How many milliliters are in 1.00 quart of

milk?

1.00 qt 1 L1.057 qt

= 946 mL

qt mL

1000 mL1 L

B. Dimensional Analysis You have 1.5 pounds of gold. Find its volume

in cm3 if the density of gold is 19.3 g/cm3.

lb cm3

1.5 lb 1 kg2.2 lb

= 35 cm31000 g

1 kg1 cm3

19.3 g

B. Dimensional Analysis How many liters of water would fill a

container that measures 75.0 in3?

75.0 in3 (2.54 cm)3

(1 in)3= 1.23 L

in3 L

1 L1000 cm3

B. Dimensional Analysis5) Your European hairdresser wants to cut your

hair 8.0 cm shorter. How many inches will he be cutting off?

8.0 cm 1 in2.54 cm

= 3.2 in

cm in

B. Dimensional Analysis

6) Taft football needs 550 cm for a 1st down. How many yards is this?

550 cm 1 in2.54 cm

= 6.0 yd

cm yd

1 ft12 in

1 yd3 ft

B. Dimensional Analysis

7) A piece of wire is 1.3 m long. How many 1.5-cm pieces can be cut from this wire?

1.3 m 100 cm1 m

= 86 pieces

cm pieces

1 piece1.5 cm