Dimensional Analysis



Dimensional Analysis

A Problem Solving Method

The Process:

1.

2.

3.

4.

5.

Example one:

55mm= _____ m

55mm__ ___1m___ = 0.055m

1. 1000mm

Example two:

88km = _____m

88km_ __1000m_ = 88,000m

1. 1km

Example two:

25km/h = _______ m/s

25km___ 1000m___ ___1h___ ___1min___ = 6.9m/s

1h 1km 60min 60s

Name _____________________

Metric Worksheet

Make the following conversions using dimensional analysis, show all your work for full credit.

1. 10 m = ________km 7. 42.3 hm = _________cm

2. 2 km = ________cm 8. 234.3 dg = _________dkg (Dg)

3. 250 mL = ______L 9. 56.82 kL = _________dL

4. 2,000 g = ________kg 10. 4.2 cm = _______dm

5. 10 kg = ________mg 11. 23.2 m = _________ Hm

6. 1,500cm3 = ________L 12. 2.6 mm = ________km

Metric Conversions

Write the answer on the line for each problem.

1) 105m = _______km 2) 23 km = _________cm

3) 25mL = _______L 4) 20g = __________kg

5) 10kg = ________mg 6) 1500mL = ____________L

7) 58cm = _______mm 8) 5mm = __________km

9) 17km = ________cm 10) 65mL = __________L

11) 128g = __________kg 12) 15kg = __________cg

13) 0.25g = ___________cg 14) 44L = _______________mL

15) 0.595 mg = ______________kg 16) 12mL = _____________cL

Problems to Solve: (refer to the equivalencies given previously)

1. Suppose a bug is 5 inches long. What is its length in feet?

2. Express a length of 320 feet in miles.

3. Express 76.874 inches in miles.

4. How many seconds are there in 782 minutes?

5. How many seconds are there in 23 days?

6. What is the length of a football field expressed in meters?

Name _______________________

Dimensional Analysis: Practice Problems (refer to the conversion factors on the previous page).

1. 7.5 lbs = ________ grams

2. 6.5 liters = ________quarts

3. 79.5 km = ________miles

4. 635976 hours = ________years

5. 7 miles = ________inches

6. 1 week = ________seconds

7. 2.5 meters = ________inches

8. 3.2 years = ________seconds

9. The capacity of the gasoline tank in an automobile is 12 gallons. How many liters is this?

10. If the price of gasoline is $0.400 per liter, what is its price per gallon?

Metric and English Conversions Worksheet

Solve the following using dimensional analysis, showing all of your work, and using the conversion factors listed.

1. How many grams are there in 457.25 pounds?

2. How many centimeters are there in 0.985 inches?

3. How many quarts are there in 2.75 L?

4. How many feet are there in 8.75 km?

5. How many milligrams are there in 62.4 ounces?

6. How many cups are there in 6.25x1022 nL? (CHALLENGE)

1. If a plane is traveling 300 miles per hour, how long will it take to travel 1800 miles?

2. If you are traveling at 60km/hr, how many centimeters per second is that equivalent to?

3. If you are running at a pace of 7.0 miles per hour, how many meters per minute is that equivalent to?

4. Convert the speed of light, 3.0 x 108 m/s, into mi/hr. (1610 m = 1 mi)

5. Convert the density of aluminum, 2.70 g/mL into kg/cm3. (1 mL = 1 cm3)

6. Convert 22.4 kg/L to kg/mL

7. What is 10095 m/s in miles/s?

8. Change 8.41 g/mL to Kg/L

9. What is 3.8 Km/sec to miles/year?

Challenge!

Dimensional Analysis

1).Convert 2.70cm3/min to L/Week

2) Convert 1.12g/cm3 to kg/dm3

3) Convert 20km/hour to m/second

4) Convert 1.87kg/dm3 to g/cm3

5) Change 2.6 km/day to m/week

6) Change 35.6 mg/cm3 to kg/L

7) Change 60 yds / hour to inches/ second

8) Change 8.3 feet/ second to yards/hour

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1 pound = 454 g 2.54 cm = 1 inch 1.06 quarts = 1 Liter

16 oz = 1 pound 12 inches = 1 foot 4 quarts = 1 gallon

3 feet = 1 yard 2 pints = 1 quart

5,280 feet = 1 mile 2 cups = 1 pint

1 pound = 454 g 2.54 cm = 1 inch 1.06 quarts = 1 Liter

16 oz = 1 pound 12 inches = 1 foot 4 quarts = 1 gallon

3 feet = 1 yard 2 pints = 1 quart

5,280 feet = 1 mile 2 cups = 1 pint

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