Unit Conversions — SAT Math Explained
The process of expressing a measurement in a different unit while keeping the value equivalent, achieved by multiplying by conversion factors (fractions equal to 1).
The Core Idea
Multiplying by a conversion factor equal to 1 (like 12 inches/1 foot = 1) doesn't change the actual quantity — only the unit of measurement. Dimensional analysis tracks units algebraically to ensure the conversion is correct.
Key Vocabulary
A fraction equal to 1, where the numerator and denominator are the same quantity in different units
Tracking units as you multiply — units cancel like factors
When the same unit appears in numerator and denominator, it cancels out
Common Conversions
1 ft = 12 in; 1 yd = 3 ft; 1 mile = 5280 ft; 1 km = 1000 m
1 lb = 16 oz; 1 ton = 2000 lb; 1 kg = 1000 g
1 gallon = 4 quarts; 1 quart = 2 pints; 1 pint = 2 cups; 1 L = 1000 mL
1 min = 60 sec; 1 hr = 60 min; 1 day = 24 hr
Process
1. Write the starting measurement as a fraction
2. Multiply by conversion factors (arranged so unwanted units cancel)
3. Continue multiplying until you have only the desired unit
4. Calculate: multiply all numerators, multiply all denominators, divide
Multi Step Example
Convert 60 miles/hour to feet/second: 60 mi/hr × 5280 ft/1 mi × 1 hr/60 min × 1 min/60 sec = 88 ft/sec
Common Errors to Avoid
Flipping the conversion factor (putting the wrong unit in the numerator)
Stopping too early in multi-step conversions
Not canceling units carefully — checking units at each step prevents errors
Practice: Unit Conversions
5 SAT-style questions. Select your answer and get an instant explanation.
Convert 3.5 kilometers to meters.
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