## Part F: Unit Analysis Problems       10 points

Back Link to Step 1 and 2     Back to Dimensional Analysis Main Menu

Apply the unit analysis method of problem solving to each of the following (setup statement 1 pt, unit analysis setup 3 pts,
answer 1 pt with its proper unit) (If greater than three significant figures round off to three significant figures):

Problem #1

How many karats is a diamond weighing 234.2 mg? (One karat = 0.200 g)

### The Question:

____???____ karat = 234.2 mg

### Given Unit Factors

• 1 karat = 0.200 g

### Unit Factors Not Given

• 1 g = 1000 mg

### The Solution:

 ??? karat = 234.2 mg X 1 g X 1 karat = 1.17 karat 1 1 1000 mg 0.200 g 1

Problem #2

Insurance statistics state that a person loses 8 minutes of average life for each cigarette smoked. If there are 20 cigarettes in a pack and the average cost of cigarette is \$4.50 per pack over the next 15 years, how many years of average life would a person lose for smoking 1.5 packs a day for 15 years?

### The Question:

____???____ yrlifelost = 15 yrsmoking

### Given Unit Factors

• 1 cig = 8 minlifelost
• 1 pack = 20 cig
• 1 pack = 4.50 dollars
• 1 day = 1.5 packsmoking

### Unit Factors Not Given

• 1 yr = 365 days (or 365.25 days)
• 1 day = 24 hr
• 1 hr = 60 min

### The Solution:

The important bridge between life lost and smoking is the 8 minutes lost = 1 cig smoked Unit Factor.

 ??? yrlifelost = 15 yrsmok X 365 daysmok X 1.5 pack X 20 cig X 8 minlost X 1 hrlost X 1 daylost X 1 yrlost = 2.5 yrlifelost 1 1 1 yrsmok 1 daysmok 1 pack 1 cig 60 minlost 24 hrlost 365 daylost 1

## Module Two-Part H: Density, Specific Gravity & Volume Problems 8 points

1. A quartz rock was cut into a rectangular solid paperweight. IF the paperweight has a mass of 165 g and measures 5.00 cm by 5.00 cm by 25.0 mm, what is its volume in cubic centimeters?

### The Question:

____???____ cm3 = 5.00 cm X 5.00 cm X 25.0 mm

10 mm = 1 cm ; therefore 25.0 mm = 2.50 cm (all units must be equal)

Volune = L3 = 5.00 cm X 5.00 cm X 2.50 cm = ____62.5__cm3

2. Calculate the density in g/mL for 10.0 grams of ethyl ether having a volume 14.0 mL.

### The Question:

Density = ____???____ g/m

Density = Mass/Volume = 10.0 g/14.0 mL = 7.14 g/mL

Link to Step 1 and 2     Back to Dimensional Analysis Main Menu