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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):
(1) How many karats is a diamond weighing
234.2 mg? (One karat = 0.200 g)
____???____ karat = 234.2 mg
Given Unit Factors

Unit Factors Not Given




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







1 
1 
1000 mg 
0.200 g 
1 


(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?
____???____ yr_{lifelost} = 15 yr_{smoking}
Given Unit Factors

Unit Factors Not Given

The important brdge between life lost and smoking is the 8
minutes _{lost} = 1 cig _{smoked} Unit Factor.



??? yr_{lifelost} 
= 
15 yr_{smok}

X 
365 day_{smok}

X 
1.5 pack 
X 
20 cig 
X 
8 min_{lost}

X 
1 hr_{lost}

X 
1 day_{lost}

X 
1 yr_{lost}

= 
2.5 yr_{lifelost} 












1 
1 
1 yr_{smok}

1 day_{smok}

1 pack 
1 cig 
60 min_{lost}

24 hr_{lost}

365 day_{lost}

1 


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?
____???____ cm^{3}
= 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 = L^{3} = 5.00 cm X 5.00 cm X 2.50 cm = ____62.5__cm^{3}
2. Calculate the density in g/mL for 10.0 grams of ethyl ether having a volume 14.0 mL.
Density = ____???____ g/m
Density = Mass/Volume = 10.0 g/14.0 mL = 7.14 g/mL
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