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### 2004-C: Conversion Factors 2: Two- and Three-Step Conversions

• Topic Cluster: Pure Mathematics
• Topic: Unit Conversion and Dimensional Analysis
• Objective: Convert a quantity to a different unit using two or three conversion factors; properly write conversion factors to show how dimensional analysis is used
• Content:
• Level: 2

#### BACK to Ladder Unit Conversion and Dimensional Analysis

Complete each of the following problems with two conversion factors. You must use two conversion factors for each problem. On some of the problems, you have to use specific conversion factors. You must follow all of the requirements for conversion problems in the study guide. Please write all answers to three significant figures of accuracy.

Whenever completing a non-metric unit conversion, explicitly write out conversion factors. When writing conversion factors:
• Quantities should be represented as fractions.
• Units should be represented as words in the correct part of a fraction.
• Conversion factors should be written as fractions with a different unit in the numerator and denominator and value equal to one.
• Units that cancel should be crossed out.
• Equal signs must be included in appropriate places.
• You should explicitly write the final answer of the conversion.
1. Convert 30 seconds to hours using two conversion factors.
2. Convert 250 seconds to hours using two conversion factors.
3. Convert 50 minutes to days.
4. Convert 1400 feet to kilometers using these conversion factors:
• 1 mile = 5280 feet
• 1 mile = 1.61 kilometers
5. Convert 1400 feet to kilometers using these different conversion factors:
• 1 meter = 3.28 feet
• 1 kilometer = 1000 meters
6. How many minutes are there in 5 days?
7. How many inches are there in 20 miles?
8. How many meters are there in 1 mile? Use these two conversion factors:
• 1 mile = 1.61 kilometers
• 1 kilometer = 1000 meters
9. How many meters are there in 1 mile? Use these two different conversion factors:
• 1 mile = 5280 feet
• 1 meter = 3.28 feet
10. Convert 500 slugs to metric tons.