🎯 Learning Objectives
- Dimensional analysis: the foolproof method to convert any unit.
- How to chain multiple conversions in a single line.
- Common metric / imperial conversions you should memorize.
- Strategies for time, distance, and currency conversions.
- Practice questions with worked solutions.
1. Why Unit Conversion Matters
On the SAT, a question may give you a speed in miles per hour and ask for the distance in feet. Or list a price in dollars per pound and ask for the cost in cents per ounce. The number changes: but the actual quantity does not. Unit conversion is just multiplication by clever forms of 1.
2. The Dimensional Analysis Recipe
Every unit conversion follows the same shape: multiply by a fraction equal to 1, where the numerator and denominator name the same quantity in different units.
Convert mph to ft/sec
60 mph × (1 hour / 60 min) × (5280 ft / 1 mile) = 88 ft/sec
STEP 1: Write the starting quantity with units
STEP 2: Multiply by a conversion fraction = 1
STEP 3: Cancel matching units like fractions
STEP 4: Whatever units remain are the answer's units
💡 Pro Tip: Track the Units, Not the Numbers
Set up the entire chain symbolically before you compute. If your final units are correct, your numerical answer is almost certainly correct too.
3. Conversions Worth Memorizing
Length
From | To | Multiply By |
1 mile | feet | 5,280 |
1 yard | feet | 3 |
1 foot | inches | 12 |
1 meter | centimeters | 100 |
1 kilometer | meters | 1,000 |
1 inch | centimeters | 2.54 (exact) |
Time
From | To | Multiply By |
1 hour | minutes | 60 |
1 minute | seconds | 60 |
1 hour | seconds | 3,600 |
1 day | hours | 24 |
1 year (non-leap) | days | 365 |
Mass / Volume
From | To | Multiply By |
1 pound | ounces | 16 |
1 kilogram | grams | 1,000 |
1 gallon | quarts | 4 |
1 quart | pints | 2 |
1 liter | milliliters | 1,000 |
4. Multi-Step Conversions
If no single conversion fraction takes you from start to finish, chain several together. Each fraction must equal 1, and each unit you don't want must cancel.
📝 Example: Cents per Ounce from Dollars per Pound
If beef costs $4.80 per pound, what is the cost in cents per ounce?
$4.80/lb × (100¢/$1) × (1 lb / 16 oz) = 480 / 16 = 30¢/oz
Notice how 'lb' and '$' cancel diagonally, leaving cents per ounce.
5. Squared and Cubed Units
When converting area or volume, you must square or cube the conversion factor. This is one of the most common mistakes on the SAT.
1 ft² = (12 in)² = 144 in² 1 ft³ = (12 in)³ = 1,728 in³
⚠️ Common Mistakes
Converting square feet to square inches with a factor of 12 (instead of 144) is the #1 unit-conversion error. Always square or cube the LINEAR conversion factor when units are squared or cubed.
6. Strategies
⚡ Memorize 60 mph = 88 ft/s
Saves a 4-step conversion every time.
⚡ 1 hour = 60 minutes = 3600 seconds
Lets you skip a multiplication step.
⚡ For temperature: 32°F = 0°C, 212°F = 100°C
Useful as quick checks.
⚡ For currency questions, multiply by the rate ONCE only
If $1 = 80 INR, then $25 = 25 × 80 = ₹2,000.
⚡ Cancel units on paper as you go
Don't trust mental tracking: cross out 'lb' and 'min' visually.
7. Summary
📌 Key Takeaways
- Method: Multiply by fractions equal to 1, with the unwanted unit on the BOTTOM.
- Goal: Make every unwanted unit cancel.
- Squared/cubed units: Square or cube the linear conversion factor.
- Useful: 60 mph = 88 ft/s; 1 inch = 2.54 cm.
8. Practice: 10 Questions
Q1. A car travels at 30 m/s. What is its speed in km/h?
A) 60 B) 90 C) 108 D) 120
Hint: 30 × 3600 / 1000 = 108.
Q2. How many seconds are in 2.5 hours?
A) 7,200 B) 8,400 C) 9,000 D) 10,800
Hint: 2.5 × 3600 = 9,000.
Q3. A bag of flour weighs 5 lb. How many ounces is that?
A) 60 B) 70 C) 80 D) 90
Hint: 5 × 16 = 80.
Q4. A field is 36 ft². How many square inches?
A) 432 B) 1,728 C) 5,184 D) 6,200
Hint: Square the factor: 36 × 144 = 5,184.
Q5. If 1 inch = 2.54 cm, how many cm in 10 inches?
A) 25.4 B) 100 C) 254 D) 2,540
Hint: 10 × 2.54 = 25.4.
Q6. A pipe carries 12 gallons per minute. How many gallons per hour?
A) 60 B) 360 C) 600 D) 720
Hint: 12 × 60 = 720.
Q7. At $0.05 per minute, what is the cost in dollars per hour?
A) $0.30 B) $1.00 C) $3.00 D) $5.00
Hint: 0.05 × 60 = $3.00/hr.
Q8. A box has volume 2 ft³. How many cubic inches?
A) 24 B) 288 C) 1,728 D) 3,456
Hint: Cube the factor: 2 × 1,728 = 3,456.
Q9. If 1 km ≈ 0.62 miles, how many miles in 50 km?
A) 25 B) 31 C) 38 D) 45
Hint: 50 × 0.62 = 31.
Q10. A printer prints 60 pages per minute. How many pages in 0.5 hours?
A) 600 B) 1,200 C) 1,800 D) 2,400
Hint: 60 × 30 = 1,800.
Answer Key & Worked Solutions
# | Answer | Reasoning |
Q1. | C) 108 | 30 m/s × 3.6 = 108 km/h. |
Q2. | C) 9,000 | 2.5 × 3,600 = 9,000. |
Q3. | C) 80 | 5 × 16 = 80. |
Q4. | C) 5,184 | 36 × 144 (= 12²) = 5,184. |
Q5. | A) 25.4 | 10 × 2.54 = 25.4. |
Q6. | D) 720 | 12 × 60 = 720. |
Q7. | C) $3.00 | $0.05 × 60 = $3.00. |
Q8. | D) 3,456 | 2 × 1,728 (= 12³) = 3,456. |
Q9. | B) 31 | 50 × 0.62 = 31. |
Q10. | C) 1,800 | 60 × 30 = 1,800. |