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CH. 2 - MEASUREMENT. III. Unit Conversions. A. Dimensional Analysis. The “Factor-Label” Method Units, or “labels” are canceled, or “factored” out. A. Dimensional Analysis. Steps: 1. Identify starting & ending units. 2. Line up conversion factors so units cancel.

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CH. 2 - MEASUREMENT

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## CH. 2 - MEASUREMENT

III. Unit Conversions

### A. Dimensional Analysis

• The “Factor-Label” Method

• Units, or “labels” are canceled, or “factored” out

### A. 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.

### A. Dimensional Analysis

• Lining up conversion factors:

= 1

1 in = 2.54 cm

2.54 cm 2.54 cm

1 =

1 in = 2.54 cm

1 in 1 in

### B. Conversion Factors

• Conversion Factors to Know:

• 1 in = 2.54 cm

• 1 mile = 2,580 ft

• 1 lb = 454 g

• 1 kg = 2.2 lbs

• 1 L = 1.06 qt

mega-

kilo-

1 M(u) =

k(u) =

103 (u)

106 (u)

BASE UNIT

deci-

(u) =

1(u) =

100

101 d(u)

centi-

1 (u) =

102 c(u)

milli-

1 (u) =

103 m(u)

micro-

1 (u) =

106 (u)

nano-

1 (u) =

109 n(u)

pico-

1 (u) =

1012 p(u)

### B. Conversion Factors

Prefix

Conversion Factor

cm

in

### C. Practice Problems

1) Your European hairdresser wants to cut your hair 8.0 cm shorter. How many inches will he be cutting off?

8.0 cm

1 in

2.54 cm

= 3.2 in

2) A light bulb requires 0.032 amps to operate. What is this quantity in milliamps?

A

mA

0.032 A

103 mA

1 A

= 32 mA

qt

mL

### C. Practice Problems

3) How many milliliters are in 1.00 quart of milk?

1 L

1.057 qt

1000 mL

1 L

1.00 qt

= 946 mL

cm

pieces

### C. Practice Problems

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

1 piece

1.5 cm

100 cm

1 m

1.3 m

= 86 pieces

5) A road race is 805 dm long. What is the length of the race in kilometers?

dm

km

1 m

102dm

1000 km

1 m

805 dm

= 8.05 x 10-2 km

cm

yd

### C. Practice Problems

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

1 ft

12 in

1 yd

3 ft

1 in

2.54 cm

550 cm

= 6.0 yd

in3

L

### C. Practice Problems

7) How many liters of water would fill a container that measures 75.0 in3?

1 L

1000 cm3

(2.54 cm)3

(1 in)3

75.0 in3

= 1.23 L

lb

cm3

### C. Practice Problems

8) You have 1.5 pounds of gold. Find its volume in cm3 if the density of gold is 19.3 g/cm3.

1 cm3

19.3 g

1 kg

2.2 lb

1000 g

1 kg

1.5 lb

= 35 cm3