Math Review: Extra problems

Write all answers with three (3) significant figures.

1)  Convert 400 ft to meters

1 meter / ´ / 400 ft / = / 121.95 meters = 122 meters
3.28 ft

2)  Convert 10 grams to µg (micrograms)

1 x106µg / × / 10 g / = / 1 x107 µg = 1.00 x107 µg
1 g

3)  Convert 5 gallons to liters

3.785 L / × / 5 gal / = / 18.9 L
1 gallon

4)  Convert 5 mph to ft/min

5 miles / × / 1 hour / × / 5280 ft / = / 26400 ft / = / 440 ft
1 hour / 60 min / 1 mile / 60 min / min

5)  Convert 5 mph to meters/seconds

5 miles / × / 1 hour / × / 1609.344 meters / = / 8046.72 meters / = / 2.2352 meters / = / 2.24 meters
1 hour / 3600 sec / 1 mile / 3600 sec / sec / sec

6)  Convert 10 grams/hr to lbs/day

10 gram / × / 1 hour / × / 1 lb / = / 10 lbs / = / 0.5289 lbs / = / 5.29x10-1 lbs
1 hour / 0.0417 days / 453.592 gram / 18.915 days / day / day

7)  Convert 10 grams/hr to tons/year

10 gram / × / 1 hour / × / 1 ton / = / 10 tons / = / 0.096692 tons / = / 9.67x10-2 tons
1 hour / 1.14x10-4 yrs / 9.072x105 gram / 103.4208 yrs / year / year

8)  How much does 5 liters of water weigh? Assume density of 1 mL of water is 1 gram.

1000 mL / × / 5 L / = / 5000 mL / = / 5000 g / = / 5.00x103 g
1 L

9)  How much does 5 gallons of gasoline weigh assuming its density is 70% of water.

1000 mL / × / 3.785 L / × / 5 gallons / × / 0.7 grams Gas / = / 13247 grams Gas
1 L / 1 gallon / 1 mL

10) How many cubic centimeters (cm3) are there in a cubic meter (m3)? How many liters (L) in a cubic meter (m3)?

100 cm / × / 100 cm / × / 100 cm / = / 1000000 cm3 / = / 1.00x106 cm3
1 meter / 1 meter / 1 meter / 1 m3 / 1 m3

1 m3 = 1000 L


Bonus Question:

Recent studies indicate that driving at speeds of 55 mph instead of 70 mph yields a 17% increase in gas mileage. If you normally drive at 70 mph on the highway, and average 20 miles/gallon, what would your gas mileage become if you started driving at 55 mph? Your vehicle has a 15-gallon tank, and you normally (when driving at 70 mph) average 300 miles on one tank of gas. You are planning a 1000-mile road trip vacation this summer, and gas costs have risen to $3.15 a gallon. Driving at the more fuel-efficient rate (55 mph), how much gas and money would you save on your trip? How much longer (in hours) would your trip take driving at 55 mph?

20 m / × / 17 / = / 3.4 mpg / 20 + 3.4 = 23.4 / 15 gallons / × / 23.4 miles / = / 351 miles
gallon / 100 / mpg @ 55 mph / tank of gas / gallon / tank of gas
3.15 d / × / 15 gal / = / 47.25 d / At 70 mph: / 47.25 d / × / 3.33 tanks / = / $157.34
Gallon / Tank / Tank / tank of gas / Trip / trip
At 55 mph: / 47.25 d / × / 2.85 tanks / = / $134.66
tank of gas / Trip / Trip

Time:

1000 mi / × / 1 hour / = / 14.3 hrs / 1000 m / × / 1 hr / = / 18.2 hrs / 18.2 - 14.3 = 3.9 hours
70 mi / 55 mi

**See accompanying spreadsheet “GasMileageAdjustments.xls” on course resources CD for automated calculations of this scenario with different values.

AIAQTP Revised: 3/4/2011