Unit conversion questions look tricky but follow one simple rule: multiply by fractions that equal 1, and cancel units like you cancel numbers. This method — dimensional analysis — works every time.
The Core Idea
A conversion factor is a fraction equal to 1:
Multiplying by 1 doesn't change the value — just the units.
One-Step Conversions
Example 1: Convert 5 feet to inches.
The "ft" cancels, leaving "in."
Multi-Step Conversions
Example 2: Convert 3 miles to inches.
Chain the fractions. Each one cancels the previous unit.
Converting Rates
Example 3: A car travels 60 miles per hour. What is the speed in feet per second?
Area and Volume Conversions
For area, square the conversion factor. For volume, cube it.
Example 4: Convert 3 square feet to square inches.
Common mistake: using 12 instead of .
Example 5: Convert 2 cubic yards to cubic feet.
SAT-Style Word Problems
Example 6: A factory produces 480 widgets per hour. How many widgets does it produce per minute?
Example 7: Water flows at a rate of 2 gallons per minute. How many gallons flow in 3 hours?
Common SAT Conversion Factors
| Conversion | Factor |
|---|---|
| 1 foot | 12 inches |
| 1 yard | 3 feet |
| 1 mile | 5,280 feet |
| 1 hour | 60 minutes |
| 1 minute | 60 seconds |
| 1 kilometer | 1,000 meters |
Practice Problems
Problem 1: Convert 45 miles per hour to miles per minute.
Solution
Problem 2: A room is 12 feet by 15 feet. What is the area in square yards?
Solution
Area = sq ft. Convert: sq yd (since ).
Problem 3: A pump moves 5 liters per minute. How many liters does it move in 2.5 hours?
Solution
liters.
Key Takeaways
- Set up conversion factors so units cancel — this prevents errors
- For area, square the conversion factor; for volume, cube it
- Chain multiple conversions by multiplying fractions
- Always check that your answer has the right units
- The SAT gives you the conversion factors in the problem — you just need the method
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